Question

Factorise:$64m^3–343n^3$.

Answer 1

Factorize the polynomial

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

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

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

Hence, the factors of $64m^3–343n^3$ are $(4m-7n)$ and $(16m^2+28mn+49n^2)$.