Question

Factorizar: 4(x + 2)2 – 5(x + 2) + 1 alternativas
(4x - 7)(x - 1)
(4x - 7)(x + 1)
(4x + 7)(x - 1)
(4x + 7)(x + 1)

Answer 1

Respuesta:

$\left(4x+7\right)\left(x+1\right)$

Explicación paso a paso:

$4\left(x+2\right)^2-5\left(x+2\right)+1$

$Expandir : \left(x+2\right)^2$

$\mathrm{Aplicar\:la\:formula\:del\:binomio\:al\:cuadrado}:\quad\left(a+b\right)^2=a^2+2ab+b^2$

$=x^2+2x\cdot \:2+2^2$

$Simplificar: x^2+2x\cdot \:2+2^2$

$=x^2+4x+2^2$ $=x^2+4x+4$

$Sustituir:$

$=4\left(x^2+4x+4\right)-5\left(x+2\right)+1$

$Expandir :4\left(x^2+4x+4\right)$

$=4x^2+4\cdot \:4x+4\cdot \:4$ $=4x^2+16x+16$

$Sustituir:$

$=4x^2+16x+16-5\left(x+2\right)+1$

$Expandir: -5\left(x+2\right)$

$\mathrm{Poner\:los\:parentesis\:utilizando}:\quad\:a\left(b+c\right)=ab+ac$

$Donde : a=-5,\:b=x,\:c=2$

$=-5x+\left(-5\right)\cdot\:2$

$\mathrm{Aplicar\:las\:reglas\:de\:los\:signos}:$   $+\left(-a\right)=-a$

$=-5x-5\cdot \:2$ $=-5x-10$

$Sustituir:$

$=4x^2+16x+16-5x-10+1$

$\mathrm{Agrupar\:terminos\:semejantes}:$

$=4x^2+16x-5x+16-10+1$

$=4x^2+11x+16-10+1$

$=4x^2+11x+7$

$=\left(4x^2+4x\right)+\left(7x+7\right)$

$Factorizar: 4x^2+4x$

$\mathrm{Aplicar\:las\:leyes\:de\:los\:exponentes}:\quad\:a^{b+c}=a^ba^c$  $:x^2=xx$

$=4xx+4x$

$\mathrm{Factorizar\:el\:termino\:comun\:} :4x$

$=4x\left(x+1\right)$

$Factorizar: 7x+7$

$\mathrm{Factorizar\:el\:termino\:comun\:} :7$

$=7\left(x+1\right)$

$Sustituir:$

$=4x\left(x+1\right)+7\left(x+1\right)$

$\mathrm{Factorizar\:el\:termino\:comun\:} :x+1$

$=\left(4x+7\right)\left(x+1\right)$

Answer 2

Respuesta:

(4x + 7)(x + 1)

Explicación paso a paso: