Question

factorise x3-1/x3

Answer 1

$$\begin{gathered} {\mathrm{x}}^3-\frac{1}{{\mathrm{x}}^3} \\ =\left(\mathrm{x}-\frac{1}{\mathrm{x}}\right)\left[{\left(\mathrm{x}\right)}^2+{\left(\frac{1}{\mathrm{x}}\right)}^2+\mathrm{x}\times \frac{1}{\mathrm{x}}\right] \\ =\left(\mathrm{x}-\frac{1}{\mathrm{x}}\right)\left({\mathrm{x}}^2+\frac{1}{{\mathrm{x}}^2}+1\right) \\ \boxed{\mathbf{Using}\mathbf{}\mathbf{Identity}\mathbf{}\mathbf{:} \\ {\mathbf{a}}^{\mathbf{3}}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{b}}^{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\left({\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\mathbf{+}\mathbf{ab}\right)} \end{gathered}$$