Question

The factorized form of a³ + (b – a)³ – b³ is ____________.

Answer 1

$$\begin{gathered} a^3+{\left(b-a\right)}^3-b^3 \\ =a^3+\left(b^3-a^3-3ba\left(b-a\right)\right)-b^3\left(\mathrm{Using}\mathrm{the}\mathrm{identity}:\hspace{0.17em}{\left(x-y\right)}^3=x^3-y^3-3xy\left(x-y\right)\right) \\ =a^3+b^3-a^3-3ba\left(b-a\right)-b^3 \\ =-3ba\left(b-a\right) \\ =3ab\left(a-b\right) \end{gathered}$$

Hence, the factorized form of a³ + (b – a)³ – b³ is 3ab(a – b).