Question

125-x⁶

(x²+1)² - 6(x²+1)² + 9

9(x+5)² - (x+7)²

9 - x² + 2xy - y²

x³ + 2x²y + xy² - 9x

x⁴ - 2x²

x⁴ - 4

Answer 1

a: \(125-x^6=\left(5-x^2\right)\left(5+5x^2+x^4\right)\)

b: \(=\left(x^2+1-3\right)^2=\left(x^2-2\right)^2\)

c: \(=\left(3x+15\right)^2-\left(x+7\right)^2\)

\(=\left(3x+15+x+7\right)\left(3x+15-x-7\right)\)

\(=\left(4x+22\right)\left(2x+8\right)\)

\(=2\left(2x+1\right)\left(x+4\right)\)

d: \(=9-\left(x-y\right)^2\)

\(=\left(3-x+y\right)\left(3+x-y\right)\)

e: \(=x\left(x^2+2xy+y^2-9\right)\)

\(=x\left(x+y-3\right)\left(x+y+3\right)\)