Question

Factorise the given polynomial:

$x^4-y^4$

Answer 1

Factorisation by using algebraic identities:

Consider the given polynomial $x^4-y^4$,

$$\begin{gathered} \because x^4-y^4={\left(x^2\right)}^2-{\left(y^2\right)}^2 \\ =\left(x^2-y^2\right)\left(x^2+y^2\right)[\because (a^2-b^2)=\left(a-b\right)\left(a+b\right)] \\ =\left(x-y\right)(x+y)\left(x^2+y^2\right)[\mathrm{Again}\mathrm{by}\mathrm{using}(a^2-b^2)=\left(a-b\right)\left(a+b\right)] \end{gathered}$$

Hence, $x^4-y^4$$=$$\left(x-y\right)(x+y)\left(x^2+y^2\right)$.