Question

Factorise: $x^4-625$

Answer 1

Using the identity $a^2-b^2=(a+b)(a-b)$

Using the above identity, the expression $x^4-625$ can be factorised as follows:

$x^4-625=(x^2{)}^2-(25{)}^2=(x^2-25)(x^2+25)=(x-5)(x+5)(x^2+25)$

Hence, $x^4-625=(x-5)(x+5)(x^2+25)$