Factorize the following expression : \((a + b)^3 – 8(a – b)^3\)
\[
(a + b)^3 – 8(a – b)^3
\]
\[
= (a + b)^3 – [2(a – b)]^3
\]
\[
= \left[(a + b) – 2(a – b)\right]
\left[(a + b)^2 + 2(a + b)(a – b) + 4(a – b)^2\right]
\]
\[
= (-a + 3b)
\left[(a + b)^2 + 2(a + b)(a – b) + 4(a – b)^2\right]
\]
\[
= (3b – a)(7a^2 – 6ab + 3b^2)
\]