Question

Question 92 (xiii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$\frac{x^2}{8}-\frac{y^2}{18}$

Answer 1

$\frac{x^2}{8}-\frac{y^2}{18}=\frac{1}{2}(\frac{x^2}{4}-\frac{y^2}{9})=\frac{1}{2}[{\left(\frac{x}{2}\right)}^2-{\left(\frac{y}{3}\right)}^2]=\frac{1}{2}(\frac{x}{2}+\frac{y}{3})(\frac{x}{2}-\frac{y}{3})$