Álgebra Ejemplos

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

Paso 1

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

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Paso 1.1

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

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

Paso 1.2

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

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

Paso 1.3

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

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

Paso 2

Aplica la propiedad distributiva.

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

Paso 3

Multiplica $4$ por $- 3$ .

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

Paso 4

Suma $4 x$ y $4 x$ .

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

Paso 5

Suma $- 12$ y $7$ .

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