Question

Factorise
x⁹ – y⁹

Answer 1

$$\begin{gathered} x^9–y^9={\left(x^3\right)}^3-{\left(y^3\right)}^3 \\ \mathrm{we}\mathrm{know} \\ {a}^3-b^3=\left(a-b\right)\left(a^2+b^2+ab\right) \\ a=x^3,b=y^3 \\ \mathrm{So},x^9–y^9={\left(x^3\right)}^3-{\left(y^3\right)}^3=\left(x^3-y^3\right)\left(x^6+y^6+x^3{y}^3\right) \\ =\left(x-y\right)\left(x^2+y^2+xy\right)\left(x^6+y^6+x^3{y}^3\right) \end{gathered}$$