Question

Using appropriate identity, simplify: 9x² + 6x + 1.

Answer 1

$$\begin{gathered} 9{\mathrm{x}}^2+6\mathrm{x}+1 \\ ={\left(3\mathrm{x}\right)}^2+2\times \left(3\mathrm{x}\right)\times \left(1\right)+{\left(1\right)}^2 \\ ={\left(3\mathrm{x}+1\right)}^2 \\ =\left(3\mathrm{x}+1\right)\left(3\mathrm{x}+1\right)\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{ab}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{b}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}{\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)}^{\mathbf{2}}\right] \end{gathered}$$