Question

Question 84 (iv)

Simplify

${(\frac{3}{4}x-\frac{4}{3}y)}^2+2xy$

Answer 1

We have,
${(\frac{3}{4}x-\frac{4}{3}y)}^2+2xy={\left(\frac{3}{4}x\right)}^2+{\left(\frac{4}{3}y\right)}^2-2\times \frac{3}{4}x\times \frac{4}{3}y+2xy$
[using the identity, $(a-b{)}^2=a^2+b^2-2ab$]
$=\frac{9}{16}{x}^2+\frac{16}{9}{y}^2-2xy+2xy=\frac{9}{16}{x}^2+\frac{16}{9}{y}^2$