Question

Factorise:
${(1-a)}^3+{\left(3a\right)}^3$

Answer 1

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

Using the above identity, the equation $(1-a{)}^3+(3a{)}^3$ can be factorised as follows:

$(1-a{)}^3+(3a{)}^3=(1-a+3a)\left[\right(1-a{)}^2+(3a{)}^2-((1-a)\times 3a\left)\right]=(1+2a)(1+a^2-2a+9a^2-3a+3a^2)$

$=(1+2a)(13a^2-5a+1)$

Hence, $(1-a{)}^3+(3a{)}^3=(1+2a)(13a^2-5a+1)$