Question

Factorise
$x^9-y^9$

Answer 1

$x^9-y^9$

Rewrite $x^9$

as $(x^3{)}^3$

.
$(x^3{)}^3-y^9$

Rewrite $y^9$
as $(y^3{)}^3$

.
$(x^3{)}^3-(y^3{)}^3$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^3-b^3=(a-b)(a^2+ab+b^2)$
where $a=x^3$ and $b=y^3$

.
$(x^3-y^3)\left(\right(x^3{)}^2+x^3{y}^3+\left(y^3{)}^2\right)$

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^3-b^3=(a-b)(a^2+ab+b^2)$
where $a=x$ and $b=y$

.
$(x-y)(x^2+xy+y^2)\left(\right(x^3{)}^2+x^3{y}^3+\left(y^3{)}^2\right)$