Question

how to complete factor 32x^5-2x

Answer 1

$32x^5-2x=2x(16x^4-1)=2x\underbrace{\left[(4x^2)^2-1^2\right]}_{use:a^2-b^2=(a-b)(a+b)}\\\\=2x(4x^2-1)(4x^2+1)=2x\underbrace{\left[(2x)^2-1^2\right]}_{use:a^2-b^2=(a-b)(a+b)}(4x^2+1)\\\\\center\boxed{=2x(2x-1)(2x+1)(4x^2+1)}$