Question

Factorise: $2x^4-32$

Answer 1

Factorization

The given expression is,

$2x^4-32=2(x^4-16)$

$=2(x^4-2^4)$

$=2\left\{{\left(x^2\right)}^2-{\left(2^2\right)}^2\right\}$

We know that,

${\mathit{a}}^{\mathbf{2}}\mathbf{-}{\mathit{b}}^{\mathbf{2}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{+}\mathit{b}\mathbf{)}\mathbf{(}\mathit{a}\mathbf{-}\mathit{b}\mathbf{)}$

$\therefore 2x^4-32=2(x^2+2^2)(x^2-2^2)$

$=2(x^2+4)(x+2)(x-2)$

Hence, the result of the factorization of the given expression is $2(x^2+4)(x+2)(x-2)$.