Question

Factorise: $a^3{b}^3+c^3$

Answer 1

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

Using the above identity, the expression $a^3{b}^3+c^3$ can be factorised as follows:

$a^3{b}^3+c^3=(ab{)}^3+(c{)}^3=(ab+c)\left[\right(ab{)}^2+(c{)}^2-(ab\times c\left)\right]=(ab+c)(a^2{b}^2+c^2-abc)$

Hence, $a^3{b}^3+c^3=(ab+c)(a^2{b}^2+c^2-abc)$