Question
Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$\frac{4\text{x}^2}{9}-\frac{9\text{y}^2}{16}$
$\frac{4\text{x}^2}{9}-\frac{9\text{y}^2}{16}$
✓
Answer
$\frac{4\text{x}^2}{9}-\frac{9\text{y}^2}{16}$$=\Big(\frac{2\text{x}}{3}\Big)^2-\Big(\frac{3\text{y}}{4}\Big)^2$
$=\Big(\frac{2\text{x}}{3}+\frac{3\text{y}}{4}\Big)\Big(\frac{2\text{x}}{3}-\frac{3\text{y}}{4}\Big)$
$=\Big(\frac{2\text{x}}{3}+\frac{3\text{y}}{4}\Big)\Big(\frac{2\text{x}}{3}-\frac{3\text{y}}{4}\Big)$
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