Question

Factorise$8a^3-b^3-12a^{2}b+6a{b}^2$

Answer 1

Factorize the polynomial

$$\begin{gathered} 8a^3-b^3-12a^{2}b+6a{b}^2 \\ ={\left(2a\right)}^3-b^3-3\times {\left(2a\right)}^2\times b+3\times 2a\times {\left(b\right)}^2 \end{gathered}$$

using the identity ${(x-y)}^3=x^3-y^3-3x^{2}y+3x{y}^2$ we have

$8a^3-b^3-12a^{3}b+6a{b}^2={(2a-b)}^3$

Hence, the factorization of $8a^3-b^3-12a^{2}b+6a{b}^2$ is ${(2a-b)}^3$.