Question

(x^2+x+4)(x^2+x+5)-(x^2+x+3)(x^2+x+6) Ayudaaa por favor

Answer 1

Respuesta:

= 2

Explicación paso a paso:

$\left(x^2+x+4\right)\left(x^2+x+5\right)-\left(x^2+x+3\right)\left(x^2+x+6\right)$

$\mathrm{Expandir}\:\left(x^2+x+4\right)\left(x^2+x+5\right):\quad x^4+2x^3+10x^2+9x+20$

$=x^4+2x^3+10x^2+9x+20-\left(x^2+x+3\right)\left(x^2+x+6\right)$

$\mathrm{Expandir}\:-\left(x^2+x+3\right)\left(x^2+x+6\right):\quad -x^4-2x^3-10x^2-9x-18$

$=x^4+2x^3+10x^2+9x+20-x^4-2x^3-10x^2-9x-18$

$\mathrm{Simplificar}\:x^4+2x^3+10x^2+9x+20-x^4-2x^3-10x^2-9x-18:\quad 2$

$=2$