Algebra Beispiele

$4 {(x - 3)}^{3} {(4 x + 7)}^{3} + {(x - 3)}^{2} {(4 x + 7)}^{4}$

Schritt 1

Faktorisiere ${(x - 3)}^{2} {(4 x + 7)}^{3}$ aus $4 {(x - 3)}^{3} {(4 x + 7)}^{3} + {(x - 3)}^{2} {(4 x + 7)}^{4}$ heraus.

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Schritt 1.1

Faktorisiere ${(x - 3)}^{2} {(4 x + 7)}^{3}$ aus $4 {(x - 3)}^{3} {(4 x + 7)}^{3}$ heraus.

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{4}$

Schritt 1.2

Faktorisiere ${(x - 3)}^{2} {(4 x + 7)}^{3}$ aus ${(x - 3)}^{2} {(4 x + 7)}^{4}$ heraus.

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 7)$

Schritt 1.3

Faktorisiere ${(x - 3)}^{2} {(4 x + 7)}^{3}$ aus ${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3)) + {(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 7)$ heraus.

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 (x - 3) + 4 x + 7)$

Schritt 2

Wende das Distributivgesetz an.

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 x + 4 \cdot - 3 + 4 x + 7)$

Schritt 3

Mutltipliziere $4$ mit $- 3$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (4 x - 12 + 4 x + 7)$

Schritt 4

Addiere $4 x$ und $4 x$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (8 x - 12 + 7)$

Schritt 5

Addiere $- 12$ und $7$ .

${(x - 3)}^{2} {(4 x + 7)}^{3} (8 x - 5)$