Question

Factorise the expression $p^4-256$

Answer 1

$p^4=(p^2{)}^2$ and $256=(16{)}^2$
Thus $p^4-256=(p^2{)}^2-(16{)}^2$
$=(p^2-16)(p^2+16)$ $[\because p^2-16=(p+4\left)\right(p-4\left)\right]$
$=(p+4)(p-4)(p^2+16)$