Question

Using appropriate identity, factorise $4x^2-\frac{y^2}{9}$

Answer 1

$4x^2-\frac{y^2}{9}$

${\left(2x\right)}^2-\left(\frac{y^2}{9}\right)$

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

$\Rightarrow {\left(2x\right)}^2-\left(\frac{y^2}{9}\right)=\left(2x+\frac{y}{3}\right)\left(2x-\frac{y}{3}\right)$

Hence, $4x^2-\frac{y^2}{9}=\left(2x+\frac{y}{3}\right)\left(2x-\frac{y}{3}\right)$

Hence, the answer is $\left(2x+\frac{y}{3}\right)\left(2x-\frac{y}{3}\right).$