Question

Question 84 (iii)

Simplify

${(\frac{7}{9}a+\frac{9}{7}b)}^2-ab$

Answer 1

We have, ${(\frac{7}{9}a+\frac{9}{7}b)}^2-ab$
$={\left(\frac{7}{9}a\right)}^2+{\left(\frac{9}{7}b\right)}^2+2\times \frac{7}{9}a\times \frac{9}{7}b-ab$ [using the identity, $(a+b{)}^2=a^2+b^2+2ab$]
$=\frac{49}{81}{a}^2+\frac{81}{49}{b}^2+2ab-ab=\frac{49}{81}{a}^2+ab+\frac{81}{49}{b}^2$