Question

Factorize: 24 root 3 x cube -125 y cube

Answer 1

$$\begin{gathered} 24\sqrt{3}{x}^3-125y^3 \\ ={\left(2\sqrt{3}x\right)}^3-{\left(5y\right)}^3 \\ =\left(2\sqrt{3}x-5y\right)\left[{\left(2\sqrt{3}x\right)}^2+2\sqrt{3}x\times 5y+{\left(5y\right)}^2\right]\{\mathrm{using}\mathrm{the}\mathrm{identity}{a}^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)\} \\ =\left(2\sqrt{3}x-5y\right)\left[12x^2+10\sqrt{3}xy+25y^2\right] \end{gathered}$$