Question

Factorise : $x^4-625$

Answer 1

Given : $x^4-625$

We can further write it as
$x^4-625$$=(x^2{)}^2-{25}^2$

Based on the equation $a^2-b^2=(a+b)(a-b)$

We get,
$x^4-625$$=(x^2+25)(x^2-25)$

On further simplification using the formula
$x^4-625$$=(x^2+25)(x^2-5^2)$

So we get,
$x^4-625$$=(x^2+25)(x+5)(x-5)$