Question

REDUCIR: (x + 1)(x - 2)(x + 3)(x + 6) – [(x^2 + 4x)^2 – 9x(x + 4)] Ayuda porfavor :(

Answer 1

Respuesta:

= -36

Explicación paso a paso:

$\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x+6\right)-\left(\left(x^2+4x\right)^2-9x\left(x+4\right)\right)$

$\mathrm{Expandir}\:\left(x^2+4x\right)^2-9x\left(x+4\right):\quad x^4+8x^3+7x^2-36x$

$=\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x+6\right)-\left(x^4+8x^3+7x^2-36x\right)$

$\mathrm{Expandir}\:\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x+6\right):\quad x^4+8x^3+7x^2-36x-36$

$=x^4+8x^3+7x^2-36x-36-\left(x^4+8x^3+7x^2-36x\right)$

$-\left(x^4+8x^3+7x^2-36x\right):\quad -x^4-8x^3-7x^2+36x$

$=x^4+8x^3+7x^2-36x-36-x^4-8x^3-7x^2+36x$

$\mathrm{Simplificar}\:x^4+8x^3+7x^2-36x-36-x^4-8x^3-7x^2+36x:\quad -36$

$=-36$