Question
Expand the following, using suitable identities.$\Big(\frac{4}{5}\text{p}+\frac{5}{3}\text{q}\Big)^2$
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Answer
$\Big(\frac{4}{5}\text{p}+\frac{5}{3}\text{q}\Big)^2$$=\Big(\frac{4}{5}\text{p}\Big)^2+\Big(\frac{5}{3}\text{q}\Big)^2+2\times\frac{4}{5}\text{p}\times\frac{5}{3}\text{q}$
$=\frac{16}{25}\text{p}^2+\frac{25}{9}\text{q}^2+\frac{8}{3}\text{pq}$
$=\frac{16}{25}\text{p}^2+\frac{25}{9}\text{q}^2+\frac{8}{3}\text{pq}$
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