Question

Use a suitable identity to get each of the following products.

$\left(3a-\frac{1}{2}\right)\left(3a-\frac{1}{2}\right)$

Answer 1

Product of algebric expression:

Solving the question,

$\left(3a-\frac{1}{2}\right)\left(3a-\frac{1}{2}\right)={\left(3a-\frac{1}{2}\right)}^2$

So, here we will use, ${\left(a-b\right)}^2=a^2+b^2-2ab$

$$\begin{gathered} {\left(3a-\frac{1}{2}\right)}^2={\left(3a\right)}^2+{\left(\frac{1}{2}\right)}^2-2\times 3a\times \frac{1}{2} \\ {\left(3a-\frac{1}{2}\right)}^2=9a^2+\frac{1}{4}-3a \end{gathered}$$

Hence, $\left(3a-\frac{1}{2}\right)\left(3a-\frac{1}{2}\right)\mathbf{=}\mathbf{9}{\mathbf{a}}^{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{4}}\mathbf{-}\mathbf{3}\mathbf{a}$.