Question

Factorise: $a^4-b^4$.

Answer 1

Factorise the polynomial

$$\begin{gathered} a^4-b^4 \\ ={\left(a^2\right)}^2-{\left(b^2\right)}^2 \end{gathered}$$

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

$a^4-b^4=(a^2-b^2)(a^2+b^2)$

again using the identity mentioned above

$a^4-b^4=(a+b)(a-b)(a^2+b^2)$

Hence the factors of $a^4-b^4$are $(a+b),(a-b)$. and $(a^2+b^2)$.