Question

Factorise:
64x^{2 _} 125

Answer 1

$$\begin{gathered} 64{\mathrm{x}}^2-125 \\ ={\left(8\mathrm{x}\right)}^2-{\left(5\sqrt{5}\right)}^2 \\ =\left(8\mathrm{x}+5\sqrt{5}\right)\left(8\mathrm{x}-5\sqrt{5}\right)\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{b}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\right] \end{gathered}$$