Question

factorise: 64x³ + 125(square root)y³

Answer 1

$$\begin{gathered} \mathrm{Assuming}\mathrm{question}\mathrm{is} \\ 64{\mathrm{x}}^3+\sqrt{125}{\mathrm{y}}^3 \\ ={\left(4\mathrm{x}\right)}^3+{\left(\sqrt{5}\mathrm{y}\right)}^3 \\ =\left(4\mathrm{x}+\sqrt{5}\mathrm{y}\right)\left[{\left(4\mathrm{x}\right)}^2-\left(4\mathrm{x}\right)\left(\sqrt{5}\mathrm{y}\right)+{\left(\sqrt{5}\mathrm{y}\right)}^2\right]\mathbf{}\left[\mathbf{Since}\mathbf{}{\mathbf{a}}^{\mathbf{3}}\mathbf{+}{\mathbf{b}}^{\mathbf{3}}\mathbf{=}\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\left({\mathbf{a}}^{\mathbf{2}}\mathbf{-}\mathbf{ab}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\right)\right] \\ =\left(4\mathrm{x}+\sqrt{5}\mathrm{y}\right)\left(16{\mathrm{x}}^2-4\sqrt{5}\mathrm{xy}+5{\mathrm{y}}^2\right) \end{gathered}$$