Question

Calcule:(x+2)^2•(3-x)^2

Answer 1

$\left(x+2\right)^2\left(3-x\right)^2\\ =\left(x^2+4x+4\right)\left(-x+3\right)^2\\ =\left(x^2+4x+4\right)\left(x^2-6x+9\right)\\ =x^2\cdot \:9+x^2\left(-6x\right)+x^2x^2+4x\cdot \:9+4x\left(-6x\right)+4xx^2+4\cdot \:9+4\left(-6x\right)+4x^2\\ =x^2\cdot \:9-x^2\cdot \:6x+x^2x^2+4x\cdot \:9-4x\cdot \:6x+4xx^2+4\cdot \:9-4\cdot \:6x+4x^2\\ =x^4-2x^3-11x^2+12x+36\\ =\left(x+2\right)\left(x^3-4x^2-3x+18\right)\\ =\left(x+2\right)\left(x+2\right)\left(x-3\right)\left(x-3\right)$ $=\left(x+2\right)^2\left(x-3\right)^2$