Question

Factorise:
$x^7+x{y}^6$

Answer 1

We know the identity $a^3+b^3=(a+b)(a^2+b^2-ab)$

Using the above identity, the equation $x^7+x{y}^6$ or $x(x^6+y^6)$ can be factorised as follows:

$x(x^6+y^6)=x\left[\right(x^2{)}^3+\left(y^2{)}^3\right]=x(x^2+y^2)\left[\right(x^2{)}^2+{\left(y^2\right)}^2-(x^2\times y^2)]=x(x^2+y^2)(x^4+y^4-x^2{y}^2)$

Hence, $x^7+x{y}^6=x(x^2+y^2)(x^4+y^4-x^2{y}^2)$