Álgebra Ejemplos

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

Paso 1

El triángulo de Pascal se puede visualizar de la siguiente manera:

$1$

$1 - 1$

$1 - 2 - 1$

$\dots$

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

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

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

El triángulo puede usarse para calcular los coeficientes de la expansión de ${(a + b)}^{n}$ al tomar el exponente $n$ y sumar $1$ . Los coeficientes se corresponderán con la línea $n + 1$ del triángulo. Para ${(\frac{1}{2} x - y)}^{10}$ , $n = 10$ de modo que los coeficientes de la expansión se corresponderán con la línea $11$ .

Paso 2

La expansión sigue la regla ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . Los valores de los coeficientes, desde el triángulo, son $1 - 10 - 45 - 120 - 210 - 252 - 210 - 120 - 45 - 10 - 1$ .

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

Paso 3

Sustituye los valores reales de $a$ , $\frac{1}{2} x$ y $b$ en la expresión $- y$ .

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

Paso 4

Simplifica cada término.

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Paso 4.1

Multiplica ${(\frac{1}{2} x)}^{10}$ por $1$ .

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

Paso 4.2

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.3

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.4

Eleva $2$ a la potencia de $10$ .

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

Paso 4.5

Aplica la regla del producto a $- y$ .

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

Paso 4.6

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.7

Cualquier valor elevado a $0$ es $1$ .

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

Paso 4.8

Multiplica $\frac{x^{10}}{1024}$ por $1$ .

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

Paso 4.9

Cualquier valor elevado a $0$ es $1$ .

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

Paso 4.10

Multiplica $\frac{x^{10}}{1024}$ por $1$ .

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

Paso 4.11

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.12

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.13

Eleva $2$ a la potencia de $9$ .

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

Paso 4.14

Cancela el factor común de $2$ .

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Paso 4.14.1

Factoriza $2$ de $10$ .

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

Paso 4.14.2

Factoriza $2$ de $512$ .

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

Paso 4.14.3

Cancela el factor común.

Paso 4.14.4

Reescribe la expresión.

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

Paso 4.15

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

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

Paso 4.16

Simplifica.

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

Paso 4.17

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.18

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

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

Paso 4.19

Mueve $5$ a la izquierda de $y$ .

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

Paso 4.20

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.21

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.22

Eleva $2$ a la potencia de $8$ .

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

Paso 4.23

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

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

Paso 4.24

Aplica la regla del producto a $- y$ .

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

Paso 4.25

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.26

Eleva $- 1$ a la potencia de $2$ .

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

Paso 4.27

Multiplica $\frac{45 x^{8}}{256}$ por $1$ .

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

Paso 4.28

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

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

Paso 4.29

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.30

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.31

Eleva $2$ a la potencia de $7$ .

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

Paso 4.32

Cancela el factor común de $8$ .

Toca para ver más pasos...

Paso 4.32.1

Factoriza $8$ de $120$ .

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

Paso 4.32.2

Factoriza $8$ de $128$ .

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

Paso 4.32.3

Cancela el factor común.

Paso 4.32.4

Reescribe la expresión.

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

Paso 4.33

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

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

Paso 4.34

Aplica la regla del producto a $- y$ .

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

Paso 4.35

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.36

Eleva $- 1$ a la potencia de $3$ .

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

Paso 4.37

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

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

Paso 4.38

Mueve $15$ a la izquierda de $y^{3}$ .

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

Paso 4.39

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.40

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.41

Eleva $2$ a la potencia de $6$ .

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

Paso 4.42

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 4.42.1

Factoriza $2$ de $210$ .

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

Paso 4.42.2

Factoriza $2$ de $64$ .

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

Paso 4.42.3

Cancela el factor común.

Paso 4.42.4

Reescribe la expresión.

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

Paso 4.43

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

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

Paso 4.44

Aplica la regla del producto a $- y$ .

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

Paso 4.45

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.46

Eleva $- 1$ a la potencia de $4$ .

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

Paso 4.47

Multiplica $\frac{105 x^{6}}{32}$ por $1$ .

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

Paso 4.48

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

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

Paso 4.49

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.50

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.51

Eleva $2$ a la potencia de $5$ .

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

Paso 4.52

Cancela el factor común de $4$ .

Toca para ver más pasos...

Paso 4.52.1

Factoriza $4$ de $252$ .

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

Paso 4.52.2

Factoriza $4$ de $32$ .

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

Paso 4.52.3

Cancela el factor común.

Paso 4.52.4

Reescribe la expresión.

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

Paso 4.53

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

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

Paso 4.54

Aplica la regla del producto a $- y$ .

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

Paso 4.55

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.56

Eleva $- 1$ a la potencia de $5$ .

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

Paso 4.57

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

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

Paso 4.58

Mueve $63$ a la izquierda de $y^{5}$ .

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

Paso 4.59

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.60

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.61

Eleva $2$ a la potencia de $4$ .

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

Paso 4.62

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 4.62.1

Factoriza $2$ de $210$ .

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

Paso 4.62.2

Factoriza $2$ de $16$ .

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

Paso 4.62.3

Cancela el factor común.

Paso 4.62.4

Reescribe la expresión.

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

Paso 4.63

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

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

Paso 4.64

Aplica la regla del producto a $- y$ .

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

Paso 4.65

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.66

Eleva $- 1$ a la potencia de $6$ .

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

Paso 4.67

Multiplica $\frac{105 x^{4}}{8}$ por $1$ .

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

Paso 4.68

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

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

Paso 4.69

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.70

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.71

Eleva $2$ a la potencia de $3$ .

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

Paso 4.72

Cancela el factor común de $8$ .

Toca para ver más pasos...

Paso 4.72.1

Factoriza $8$ de $120$ .

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

Paso 4.72.2

Cancela el factor común.

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

Paso 4.72.3

Reescribe la expresión.

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

Paso 4.73

Aplica la regla del producto a $- y$ .

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

Paso 4.74

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.75

Eleva $- 1$ a la potencia de $7$ .

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

Paso 4.76

Multiplica $15$ por $- 1$ .

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

Paso 4.77

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.78

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.79

Eleva $2$ a la potencia de $2$ .

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

Paso 4.80

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

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

Paso 4.81

Aplica la regla del producto a $- y$ .

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

Paso 4.82

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.83

Eleva $- 1$ a la potencia de $8$ .

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

Paso 4.84

Multiplica $\frac{45 x^{2}}{4}$ por $1$ .

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

Paso 4.85

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

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

Paso 4.86

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.87

Simplifica.

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

Paso 4.88

Cancela el factor común de $2$ .

Toca para ver más pasos...

Paso 4.88.1

Factoriza $2$ de $10$ .

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

Paso 4.88.2

Cancela el factor común.

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

Paso 4.88.3

Reescribe la expresión.

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

Paso 4.89

Aplica la regla del producto a $- y$ .

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

Paso 4.90

Reescribe con la propiedad conmutativa de la multiplicación.

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

Paso 4.91

Eleva $- 1$ a la potencia de $9$ .

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

Paso 4.92

Multiplica $5$ por $- 1$ .

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

Paso 4.93

Multiplica ${(\frac{1}{2} x)}^{0}$ por $1$ .

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

Paso 4.94

Combina $\frac{1}{2}$ y $x$ .

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

Paso 4.95

Aplica la regla del producto a $\frac{x}{2}$ .

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

Paso 4.96

Cualquier valor elevado a $0$ es $1$ .

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

Paso 4.97

Cualquier valor elevado a $0$ es $1$ .

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

Paso 4.98

Divide $1$ por $1$ .

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

Paso 4.99

Multiplica ${(- y)}^{10}$ por $1$ .

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

Paso 4.100

Aplica la regla del producto a $- y$ .

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

Paso 4.101

Eleva $- 1$ a la potencia de $10$ .

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

Paso 4.102

Multiplica $y^{10}$ por $1$ .

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