Question

Question 85 (v)

Expand the following, using suitable identities.

${(\frac{4}{5}p+\frac{5}{3}q)}^2$

Answer 1

We have,
${(\frac{4}{5}p+\frac{5}{3}q)}^2={\left(\frac{4}{5}p\right)}^2+{\left(\frac{5}{3}q\right)}^2+2\times \frac{4}{5}$
$p\times \frac{5}{3}q$
$=\frac{16}{25}{p}^2+\frac{25}{9}{q}^2+\frac{8}{3}pq$
[using the identity, $(a+b{)}^2=a^2+b^2+2ab$]