Question

Factorise:
$x^3-512$

Answer 1

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

Using the above identity, the equation $x^3-512$ can be factorised as follows:

$x^3-512=(x{)}^3-{\left(8\right)}^3=(x-8)\left[\right(x{)}^2+{\left(8\right)}^2+(x\times 8)]=(x-8)(x^2+64+8x)$

Hence, $x^3-512=(x-8)(x^2+64+8x)$