Question

Factorize the following: $64m^3-343n^3$.

Answer 1

Factorize the given polynomial

$64m^3-343n^3={\left(4m\right)}^3-{\left(7n\right)}^3$

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

$$\begin{gathered} \therefore 64m^3-343n^3=(4m-7n)({\left(4m\right)}^2+{\left(7n\right)}^2+\left(4m\right)\left(7n\right)) \\ =(4m-7n)(16m^2+49n^2+28mn) \end{gathered}$$

Hence, the factorized form of the polynomial $64m^3-343n^3$ is $(4m-7n)$$(16m^2+49n^2+28mn)$.