Álgebra Ejemplos

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

Paso 1

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

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Paso 1.1

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

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

Paso 1.2

Factoriza ${(x - 5)}^{3} {(7 x + 3)}^{3}$ de ${(x - 5)}^{4} {(7 x + 3)}^{3}$ .

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

Paso 1.3

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

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

Paso 2

Aplica la propiedad distributiva.

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

Paso 3

Multiplica $7$ por $6$ .

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

Paso 4

Multiplica $6$ por $3$ .

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

Paso 5

Suma $42 x$ y $x$ .

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

Paso 6

Resta $5$ de $18$ .

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