Question

Question 85 (iv)

Expand the following, using suitable identities.

${(\frac{2}{3}x-\frac{3}{2}y)}^2$

Answer 1

We have,
${(\frac{2}{3}x-\frac{3}{2}y)}^2={\left(\frac{2}{3}x\right)}^2+{\left(\frac{3}{2}y\right)}^2-2\times \frac{2}{3}x\times \frac{3}{2}y$
[using the identity, $(a-b{)}^2=a^2+b^2-2ab$]
$=\frac{4}{9}{x}^2+\frac{9}{4}{y}^2-2xy$