Álgebra Ejemplos

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

Paso 1

Factoriza ${(2 x + 3)}^{2} {(x - 7)}^{3}$ de $8 {(2 x + 3)}^{2} {(x - 7)}^{4} - {(2 x + 3)}^{3} {(x - 7)}^{3}$ .

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Paso 1.1

Factoriza ${(2 x + 3)}^{2} {(x - 7)}^{3}$ de $8 {(2 x + 3)}^{2} {(x - 7)}^{4}$ .

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

Paso 1.2

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

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

Paso 1.3

Factoriza ${(2 x + 3)}^{2} {(x - 7)}^{3}$ de ${(2 x + 3)}^{2} {(x - 7)}^{3} (8 (x - 7)) + {(2 x + 3)}^{2} {(x - 7)}^{3} (- (2 x + 3))$ .

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

Paso 2

Aplica la propiedad distributiva.

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x + 8 \cdot - 7 - (2 x + 3))$

Paso 3

Multiplica $8$ por $- 7$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - (2 x + 3))$

Paso 4

Aplica la propiedad distributiva.

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - (2 x) - 1 \cdot 3)$

Paso 5

Multiplica $2$ por $- 1$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - 2 x - 1 \cdot 3)$

Paso 6

Multiplica $- 1$ por $3$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (8 x - 56 - 2 x - 3)$

Paso 7

Resta $2 x$ de $8 x$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (6 x - 56 - 3)$

Paso 8

Resta $3$ de $- 56$ .

${(2 x + 3)}^{2} {(x - 7)}^{3} (6 x - 59)$