Question
Expand the following, using suitable identities.$\Big(\frac{2}{3}\text{x}-\frac{3}{2}\text{y}\Big)^2$
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Answer
$\Big(\frac{2}{3}\text{x}-\frac{3}{2}\text{y}\Big)^2$$=\Big(\frac{2}{3}\text{x}\Big)^2+\Big(\frac{3}{2}\text{y}\Big)^2-2\times\frac{2}{3}\text{x}\times\frac{3}{2}\text{y}$
$=\frac{4}{9}\text{x}^2+\frac{9}{4}\text{y}^2-2\text{xy}$
$=\frac{4}{9}\text{x}^2+\frac{9}{4}\text{y}^2-2\text{xy}$
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