Question

Factorise the following expression: $a^4-2a^2{b}^2+b^4$

Answer 1

Factorise by using identities

Given, $a^4-2a^2{b}^2+b^4$

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

So, upon comparison with this identity, we get

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

Therefore, the factorisation of $a^4-2a^2{b}^2+b^4$ will be ${(a^2-b^2)}^2$.