Algebra Esempi

${(\frac{1}{2} x - y)}^{10}$

Passaggio 1

Il triangolo di Tartaglia può essere visualizzato come segue:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

$1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1$

$1 - 9 - 36 - 84 - 126 - 126 - 84 - 36 - 9 - 1$

$1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1$

È possibile utilizzare il triangolo per calcolare i coefficienti dell'espansione di ${(a + b)}^{n}$ prendendo l'esponente $n$ e sommando $1$ . I coefficienti corrisponderanno alla linea $n + 1$ del triangolo. Per ${(\frac{1}{2} x - y)}^{10}$ , $n = 10$ in modo che i coefficienti dell'espansione corrispondano alla linea $11$ .

Passaggio 2

L'espansione segue la regola ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . I valori dei coefficienti dal triangolo sono $1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1$ .

$1 a^{10} b^{0} + 10 a^{9} b + 45 a^{8} b^{2} + 120 a^{7} b^{3} + 210 a^{6} b^{4} + 252 a^{5} b^{5} + 210 a^{4} b^{6} + 120 a^{3} b^{7} + 45 a^{2} b^{8} + 10 a b^{9} + 1 a^{0} b^{10}$

Passaggio 3

Sostituisci i valori effettivi di $a$ $\frac{1}{2} x$ e $b$ $- y$ nell'espressione.

$1 {(\frac{1}{2} x)}^{10} {(- y)}^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4

Semplifica ciascun termine.

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Passaggio 4.1

Moltiplica ${(\frac{1}{2} x)}^{10}$ per $1$ .

${(\frac{1}{2} x)}^{10} {(- y)}^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.2

$\frac{1}{2}$ e $x$ .

${(\frac{x}{2})}^{10} {(- y)}^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.3

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{2^{10}} {(- y)}^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.4

Eleva $2$ alla potenza di $10$ .

$\frac{x^{10}}{1024} {(- y)}^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.5

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} ({(- 1)}^{0} y^{0}) + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.6

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

${(- 1)}^{0} \frac{x^{10}}{1024} y^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.7

Qualsiasi valore elevato a $0$ è $1$ .

$1 \frac{x^{10}}{1024} y^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.8

Moltiplica $\frac{x^{10}}{1024}$ per $1$ .

$\frac{x^{10}}{1024} y^{0} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.9

Qualsiasi valore elevato a $0$ è $1$ .

$\frac{x^{10}}{1024} \cdot 1 + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.10

Moltiplica $\frac{x^{10}}{1024}$ per $1$ .

$\frac{x^{10}}{1024} + 10 {(\frac{1}{2} x)}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.11

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} + 10 {(\frac{x}{2})}^{9} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.12

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} + 10 \frac{x^{9}}{2^{9}} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.13

Eleva $2$ alla potenza di $9$ .

$\frac{x^{10}}{1024} + 10 \frac{x^{9}}{512} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.14

Elimina il fattore comune di $2$ .

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Passaggio 4.14.1

Scomponi $2$ da $10$ .

$\frac{x^{10}}{1024} + 2 (5) \frac{x^{9}}{512} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.14.2

Scomponi $2$ da $512$ .

$\frac{x^{10}}{1024} + 2 \cdot 5 \frac{x^{9}}{2 \cdot 256} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.14.3

Elimina il fattore comune.

Passaggio 4.14.4

Riscrivi l'espressione.

$\frac{x^{10}}{1024} + 5 \frac{x^{9}}{256} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.15

$5$ e $\frac{x^{9}}{256}$ .

$\frac{x^{10}}{1024} + \frac{5 x^{9}}{256} {(- y)}^{1} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.16

Semplifica.

$\frac{x^{10}}{1024} + \frac{5 x^{9}}{256} (- y) + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.17

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 x^{9}}{256} y + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.18

$y$ e $\frac{5 x^{9}}{256}$ .

$\frac{x^{10}}{1024} - \frac{y (5 x^{9})}{256} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.19

Sposta $5$ alla sinistra di $y$ .

$\frac{x^{10}}{1024} - \frac{5 \cdot y x^{9}}{256} + 45 {(\frac{1}{2} x)}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.20

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + 45 {(\frac{x}{2})}^{8} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.21

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + 45 \frac{x^{8}}{2^{8}} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.22

Eleva $2$ alla potenza di $8$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + 45 \frac{x^{8}}{256} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.23

$45$ e $\frac{x^{8}}{256}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8}}{256} {(- y)}^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.24

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8}}{256} ({(- 1)}^{2} y^{2}) + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.25

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + {(- 1)}^{2} \frac{45 x^{8}}{256} y^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.26

Eleva $- 1$ alla potenza di $2$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + 1 \frac{45 x^{8}}{256} y^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.27

Moltiplica $\frac{45 x^{8}}{256}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8}}{256} y^{2} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.28

$\frac{45 x^{8}}{256}$ e $y^{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 120 {(\frac{1}{2} x)}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.29

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 120 {(\frac{x}{2})}^{7} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.30

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 120 \frac{x^{7}}{2^{7}} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.31

Eleva $2$ alla potenza di $7$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 120 \frac{x^{7}}{128} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.32

Elimina il fattore comune di $8$ .

Tocca per altri passaggi...

Passaggio 4.32.1

Scomponi $8$ da $120$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 8 (15) \frac{x^{7}}{128} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.32.2

Scomponi $8$ da $128$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 8 \cdot 15 \frac{x^{7}}{8 \cdot 16} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.32.3

Elimina il fattore comune.

Passaggio 4.32.4

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + 15 \frac{x^{7}}{16} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.33

$15$ e $\frac{x^{7}}{16}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + \frac{15 x^{7}}{16} {(- y)}^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.34

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + \frac{15 x^{7}}{16} ({(- 1)}^{3} y^{3}) + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.35

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} + {(- 1)}^{3} \frac{15 x^{7}}{16} y^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.36

Eleva $- 1$ alla potenza di $3$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 x^{7}}{16} y^{3} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.37

$y^{3}$ e $\frac{15 x^{7}}{16}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{y^{3} (15 x^{7})}{16} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.38

Sposta $15$ alla sinistra di $y^{3}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 \cdot y^{3} x^{7}}{16} + 210 {(\frac{1}{2} x)}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.39

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 210 {(\frac{x}{2})}^{6} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.40

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 210 \frac{x^{6}}{2^{6}} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.41

Eleva $2$ alla potenza di $6$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 210 \frac{x^{6}}{64} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.42

Elimina il fattore comune di $2$ .

Tocca per altri passaggi...

Passaggio 4.42.1

Scomponi $2$ da $210$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 2 (105) \frac{x^{6}}{64} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.42.2

Scomponi $2$ da $64$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 2 \cdot 105 \frac{x^{6}}{2 \cdot 32} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.42.3

Elimina il fattore comune.

Passaggio 4.42.4

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 105 \frac{x^{6}}{32} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.43

$105$ e $\frac{x^{6}}{32}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6}}{32} {(- y)}^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.44

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6}}{32} ({(- 1)}^{4} y^{4}) + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.45

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + {(- 1)}^{4} \frac{105 x^{6}}{32} y^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.46

Eleva $- 1$ alla potenza di $4$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + 1 \frac{105 x^{6}}{32} y^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.47

Moltiplica $\frac{105 x^{6}}{32}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6}}{32} y^{4} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.48

$\frac{105 x^{6}}{32}$ e $y^{4}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 252 {(\frac{1}{2} x)}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.49

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 252 {(\frac{x}{2})}^{5} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.50

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 252 \frac{x^{5}}{2^{5}} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.51

Eleva $2$ alla potenza di $5$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 252 \frac{x^{5}}{32} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.52

Elimina il fattore comune di $4$ .

Tocca per altri passaggi...

Passaggio 4.52.1

Scomponi $4$ da $252$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 4 (63) \frac{x^{5}}{32} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.52.2

Scomponi $4$ da $32$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 4 \cdot 63 \frac{x^{5}}{4 \cdot 8} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.52.3

Elimina il fattore comune.

Passaggio 4.52.4

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + 63 \frac{x^{5}}{8} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.53

$63$ e $\frac{x^{5}}{8}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + \frac{63 x^{5}}{8} {(- y)}^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.54

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + \frac{63 x^{5}}{8} ({(- 1)}^{5} y^{5}) + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.55

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} + {(- 1)}^{5} \frac{63 x^{5}}{8} y^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.56

Eleva $- 1$ alla potenza di $5$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 x^{5}}{8} y^{5} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.57

$y^{5}$ e $\frac{63 x^{5}}{8}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{y^{5} (63 x^{5})}{8} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.58

Sposta $63$ alla sinistra di $y^{5}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 \cdot y^{5} x^{5}}{8} + 210 {(\frac{1}{2} x)}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.59

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 210 {(\frac{x}{2})}^{4} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.60

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 210 \frac{x^{4}}{2^{4}} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.61

Eleva $2$ alla potenza di $4$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 210 \frac{x^{4}}{16} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.62

Elimina il fattore comune di $2$ .

Tocca per altri passaggi...

Passaggio 4.62.1

Scomponi $2$ da $210$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 2 (105) \frac{x^{4}}{16} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.62.2

Scomponi $2$ da $16$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 2 \cdot 105 \frac{x^{4}}{2 \cdot 8} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.62.3

Elimina il fattore comune.

Passaggio 4.62.4

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 105 \frac{x^{4}}{8} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.63

$105$ e $\frac{x^{4}}{8}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4}}{8} {(- y)}^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.64

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4}}{8} ({(- 1)}^{6} y^{6}) + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.65

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + {(- 1)}^{6} \frac{105 x^{4}}{8} y^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.66

Eleva $- 1$ alla potenza di $6$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + 1 \frac{105 x^{4}}{8} y^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.67

Moltiplica $\frac{105 x^{4}}{8}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4}}{8} y^{6} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.68

$\frac{105 x^{4}}{8}$ e $y^{6}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 120 {(\frac{1}{2} x)}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.69

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 120 {(\frac{x}{2})}^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.70

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 120 \frac{x^{3}}{2^{3}} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.71

Eleva $2$ alla potenza di $3$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 120 \frac{x^{3}}{8} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.72

Elimina il fattore comune di $8$ .

Tocca per altri passaggi...

Passaggio 4.72.1

Scomponi $8$ da $120$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 8 (15) \frac{x^{3}}{8} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.72.2

Elimina il fattore comune.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 8 \cdot 15 \frac{x^{3}}{8} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.72.3

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 15 x^{3} {(- y)}^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.73

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 15 x^{3} ({(- 1)}^{7} y^{7}) + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.74

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 15 \cdot {(- 1)}^{7} x^{3} y^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.75

Eleva $- 1$ alla potenza di $7$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} + 15 \cdot - 1 x^{3} y^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.76

Moltiplica $15$ per $- 1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + 45 {(\frac{1}{2} x)}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.77

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + 45 {(\frac{x}{2})}^{2} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.78

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + 45 \frac{x^{2}}{2^{2}} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.79

Eleva $2$ alla potenza di $2$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + 45 \frac{x^{2}}{4} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.80

$45$ e $\frac{x^{2}}{4}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2}}{4} {(- y)}^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.81

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2}}{4} ({(- 1)}^{8} y^{8}) + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.82

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + {(- 1)}^{8} \frac{45 x^{2}}{4} y^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.83

Eleva $- 1$ alla potenza di $8$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + 1 \frac{45 x^{2}}{4} y^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.84

Moltiplica $\frac{45 x^{2}}{4}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2}}{4} y^{8} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.85

$\frac{45 x^{2}}{4}$ e $y^{8}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 10 {(\frac{1}{2} x)}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.86

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 10 {(\frac{x}{2})}^{1} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.87

Semplifica.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 10 \frac{x}{2} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.88

Elimina il fattore comune di $2$ .

Tocca per altri passaggi...

Passaggio 4.88.1

Scomponi $2$ da $10$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 2 (5) \frac{x}{2} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.88.2

Elimina il fattore comune.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 2 \cdot 5 \frac{x}{2} {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.88.3

Riscrivi l'espressione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 5 x {(- y)}^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.89

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 5 x ({(- 1)}^{9} y^{9}) + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.90

Riscrivi utilizzando la proprietà commutativa della moltiplicazione.

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 5 \cdot {(- 1)}^{9} x y^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.91

Eleva $- 1$ alla potenza di $9$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} + 5 \cdot - 1 x y^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.92

Moltiplica $5$ per $- 1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + 1 {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.93

Moltiplica ${(\frac{1}{2} x)}^{0}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + {(\frac{1}{2} x)}^{0} {(- y)}^{10}$

Passaggio 4.94

$\frac{1}{2}$ e $x$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + {(\frac{x}{2})}^{0} {(- y)}^{10}$

Passaggio 4.95

Applica la regola del prodotto a $\frac{x}{2}$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + \frac{x^{0}}{2^{0}} {(- y)}^{10}$

Passaggio 4.96

Qualsiasi valore elevato a $0$ è $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + \frac{1}{2^{0}} {(- y)}^{10}$

Passaggio 4.97

Qualsiasi valore elevato a $0$ è $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + \frac{1}{1} {(- y)}^{10}$

Passaggio 4.98

Dividi $1$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + 1 {(- y)}^{10}$

Passaggio 4.99

Moltiplica ${(- y)}^{10}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + {(- y)}^{10}$

Passaggio 4.100

Applica la regola del prodotto a $- y$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + {(- 1)}^{10} y^{10}$

Passaggio 4.101

Eleva $- 1$ alla potenza di $10$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + 1 y^{10}$

Passaggio 4.102

Moltiplica $y^{10}$ per $1$ .

$\frac{x^{10}}{1024} - \frac{5 y x^{9}}{256} + \frac{45 x^{8} y^{2}}{256} - \frac{15 y^{3} x^{7}}{16} + \frac{105 x^{6} y^{4}}{32} - \frac{63 y^{5} x^{5}}{8} + \frac{105 x^{4} y^{6}}{8} - 15 x^{3} y^{7} + \frac{45 x^{2} y^{8}}{4} - 5 x y^{9} + y^{10}$