Question

reduce R= (x-3)(x+2)(x-5)(x+4) -(x-2)²(x+1)²+22x(x+1)

Answer 1

Respuesta:

$=44x+116$

Explicación paso a paso:

$\left(x-3\right)\left(x+2\right)\left(x-5\right)\left(x+4\right)-\left(x-2\right)^2\left(x+1\right)^2+22x\left(x+1\right)\\\\=\left(x-3\right)\left(x+2\right)\left(x-5\right)\left(x+4\right)-\left(x^2-4x+4\right)\left(x+1\right)^2+22x\left(x+1\right)\\\\=\left(x-3\right)\left(x+2\right)\left(x-5\right)\left(x+4\right)-\left(x^2-4x+4\right)\left(x^2+2x+1\right)+22x\left(x+1\right)\\\\=x^4-2x^3-25x^2+26x+120-x^4+2x^3+3x^2-4x-4+22x\left(x+1\right)$

$=x^4-2x^3-25x^2+26x+120-x^4+2x^3+3x^2-4x-4+22x^2+22x\\\\=44x+116$