Question
Factorise:
$x^9-y^9$
$x^9-y^9$
✓
Answer
$x^9-y^9$
$=\left(x^3\right)^3-\left(y^3\right)^3$
$=\left[\left(x^3-y^3\right)\right]\left[\left(x^3\right)^2+x^3 y^3+\left(y^3\right)^2\right]$
$=\left[(x-y)\left(x^2+x y+y^2\right)\left(x^6+x^3 y^3+y^6\right)\right.$
$=\left(x^3\right)^3-\left(y^3\right)^3$
$=\left[\left(x^3-y^3\right)\right]\left[\left(x^3\right)^2+x^3 y^3+\left(y^3\right)^2\right]$
$=\left[(x-y)\left(x^2+x y+y^2\right)\left(x^6+x^3 y^3+y^6\right)\right.$
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