Question

Factorize using appropriate identities
$\frac{9}{16}{x}^2-\frac{y^2}{9}$

Answer 1

We know $\frac{9}{16}{x}^2-\frac{y^2}{9}$ $={\left(\frac{3}{4}x\right)}^2-{\left(\frac{y}{3}\right)}^2$

Using identity $a^2-b^2=(a+b)(a-b)$

Here $a=\frac{3}{4}x$ and $b=\frac{y}{3}$

Therefore, the value of ${\left(\frac{3}{4}x\right)}^2-{\left(\frac{y}{3}\right)}^2$ is

$=(\frac{3}{4}x+\frac{y}{3})(\frac{3}{4}x-\frac{y}{3})$