Question
Factorise:
$2 x^4-32$
$2 x^4-32$
✓
Answer
$2 x^4-32$
$=2\left(x^4-16\right)$
$=2\left[\left(x^2\right)^2-(4)^2\right]$
$=2\left[\left(x^2-4\right)\left(x^2+4\right)\right]$
$=2\left[\left(x^2-2^2\right)\left(x^2+4\right)\right]$
$=2\left[(x-2)(x+2)\left(x^2+4\right)\right]$
$=2(x-2)(x+2)\left(x^2+4\right)$
$=2\left(x^4-16\right)$
$=2\left[\left(x^2\right)^2-(4)^2\right]$
$=2\left[\left(x^2-4\right)\left(x^2+4\right)\right]$
$=2\left[\left(x^2-2^2\right)\left(x^2+4\right)\right]$
$=2\left[(x-2)(x+2)\left(x^2+4\right)\right]$
$=2(x-2)(x+2)\left(x^2+4\right)$
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