Question

Factorise the following expression: $a^4-b^4$

Answer 1

Factorise by using identities

Given, $a^4-b^4$

We know that $a^2-b^2=(a-b)(a+b)$

Now, upon comparing $a^4-b^4$ with this identity, we get

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

Therefore, $a^4-b^4$ can be factorised as $(a-b)(a+b)(a^2+b^2)$.