Question

Factorize the following: $27y^3+125z^3$.

Answer 1

Factorize the given polynomial

$$\begin{gathered} 27y^3+125z^3 \\ ={\left(3y\right)}^3+{\left(5z\right)}^3 \end{gathered}$$

Use the identity ${\mathit{a}}^{\mathbf{3}}\mathbf{+}{\mathit{b}}^{\mathbf{3}}\mathbf{=}\mathbf{(}\mathit{a}\mathbf{+}\mathit{b}\mathbf{)}\mathbf{(}{\mathit{a}}^{\mathbf{2}}\mathbf{+}{\mathit{b}}^{\mathbf{2}}\mathbf{-}\mathit{a}\mathit{b}\mathbf{)}$

$27y^3+125z^3=(3y+5z)(9y^2+25z^2-15yz)$

Hence, the factor of the polynomial $27y^3+125z^3$ are $(3y+5z)$ and$(9y^2+25z^2-15yz)$.