Algebra Beispiele

$6 {(x - 5)}^{3} {(7 x + 3)}^{4} + {(x - 5)}^{4} {(7 x + 3)}^{3}$

Schritt 1

Faktorisiere ${(x - 5)}^{3} {(7 x + 3)}^{3}$ aus $6 {(x - 5)}^{3} {(7 x + 3)}^{4} + {(x - 5)}^{4} {(7 x + 3)}^{3}$ heraus.

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Schritt 1.1

Faktorisiere ${(x - 5)}^{3} {(7 x + 3)}^{3}$ aus $6 {(x - 5)}^{3} {(7 x + 3)}^{4}$ heraus.

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{4} {(7 x + 3)}^{3}$

Schritt 1.2

Faktorisiere ${(x - 5)}^{3} {(7 x + 3)}^{3}$ aus ${(x - 5)}^{4} {(7 x + 3)}^{3}$ heraus.

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{3} {(7 x + 3)}^{3} (x - 5)$

Schritt 1.3

Faktorisiere ${(x - 5)}^{3} {(7 x + 3)}^{3}$ aus ${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3)) + {(x - 5)}^{3} {(7 x + 3)}^{3} (x - 5)$ heraus.

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x + 3) + x - 5)$

Schritt 2

Wende das Distributivgesetz an.

${(x - 5)}^{3} {(7 x + 3)}^{3} (6 (7 x) + 6 \cdot 3 + x - 5)$

Schritt 3

Mutltipliziere $7$ mit $6$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (42 x + 6 \cdot 3 + x - 5)$

Schritt 4

Mutltipliziere $6$ mit $3$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (42 x + 18 + x - 5)$

Schritt 5

Addiere $42 x$ und $x$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (43 x + 18 - 5)$

Schritt 6

Subtrahiere $5$ von $18$ .

${(x - 5)}^{3} {(7 x + 3)}^{3} (43 x + 13)$