Question

$\begin{array}{cc}\text{Factorise.}& \\ \text{(i)}{a}^4-b^4& \text{(ii)}{p}^4-81\end{array}$

Answer 1

(i) $a^4-b^4$

= $(a^2{)}^2-(b^2{)}^2$

= $(a^2-b^2)(a^2+b^2)$

= $(a-b)(a+b)(a^2+b^2)$

(ii) $p^4-81$

= $(p^2{)}^2-(q^2)$

= $(p^2-q)(p^2+q)$

= $(p^2-3^2)(p^2+q)$

= $(p-3)(p+3)(p^2+q)$