Question

Factorise:
$z^4{x}^3+8y^3{z}^4$

Answer 1

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

Using the above identity, the equation $z^4{x}^3+8y^3{z}^4$ can be factorised as follows:

$z^4{x}^3+8y^3{z}^4=z^4(x^3-8y^3)=z^4\left[\right(x{)}^3+\left(2y{)}^3\right]=z^4(x+2y)\left[\right(x{)}^2+{\left(2y\right)}^2-(x\times 2y)]$

$=z^4(x+2y)(x^2+4y^2-2xy)$

Hence, $z^4{x}^3+8y^3{z}^4=z^4(x+2y)(x^2+4y^2-2xy)$