Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\frac{\text{x}^2}{9}-\frac{\text{y}^2}{25}$
$\frac{\text{x}^2}{9}-\frac{\text{y}^2}{25}$
✓
Answer
$\frac{\text{x}^2}{9}-\frac{\text{y}^2}{25}$$=\Big(\frac{\text{x}}{3}\Big)^2-\Big(\frac{\text{y}}{5}\Big)^2$
$=\Big(\frac{\text{x}}{3}-\frac{\text{y}}{5}\Big)\Big(\frac{\text{x}}{3}+\frac{\text{y}}{5}\Big)$
$=\Big(\frac{\text{x}}{3}-\frac{\text{y}}{5}\Big)\Big(\frac{\text{x}}{3}+\frac{\text{y}}{5}\Big)$
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