Question

Question 85 (iii)

Expand the following, using suitable identities.

${(\frac{4}{5}a+\frac{5}{4}b)}^2$

Answer 1

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