Question

simplify (x+3) + (x+3) (x-3 ) using identities.

Answer 1

$$\begin{gathered} \left(\mathrm{x}+3\right)+\left(\mathrm{x}+3\right)\left(\mathrm{x}-3\right)=\left(\mathrm{x}+3\right)+{\mathrm{x}}^2-9\left[\mathrm{Using}\mathrm{identity},{\mathrm{a}}^2-{\mathrm{b}}^2=\left(\mathrm{a}-\mathrm{b}\right)\left(\mathrm{a}+\mathrm{b}\right)\right] \\ ={\mathrm{x}}^2-6 \\ ={\mathrm{x}}^2-{\left(\sqrt{6}\right)}^2 \\ =\left(\mathrm{x}-\sqrt{6}\right)\left(\mathrm{x}+\sqrt{6}\right) \\ \mathrm{Thus},\mathbf{}\left(\mathbf{x}\mathbf{+}\mathbf{3}\right)\mathbf{+}\left(\mathbf{x}\mathbf{+}\mathbf{3}\right)\left(\mathbf{x}\mathbf{-}\mathbf{3}\right)\mathbf{=}\left(\mathbf{x}\mathbf{-}\sqrt{\mathbf{6}}\right)\left(\mathbf{x}\mathbf{+}\sqrt{\mathbf{6}}\right) \end{gathered}$$