Question

Resolve into factors of $x^6-y^6$

Answer 1

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

$\&$ $a^3-b^3=(a-b)(a^2+ab+b^2)$

$\therefore x^6-y^6={\left(x^2\right)}^3-{\left(y^2\right)}^3$

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

$\Rightarrow x^6-y^6=(x^2-y^2)({\left(x^2\right)}^3+x^2{\left(y\right)}^2+{\left(y^2\right)}^2)$

Hence, the answer is $(x^2-y^2)({\left(x^2\right)}^3+x^2{\left(y\right)}^2+{\left(y^2\right)}^2).$