Question

Question 85 (viii)

Expand the following, using suitable identities.

$(\frac{4x}{5}+\frac{y}{4})(\frac{4x}{5}+\frac{3y}{4})$

Answer 1

We have,
$(\frac{4x}{5}+\frac{y}{4})(\frac{4x}{5}+\frac{3y}{4})={\left(\frac{4x}{5}\right)}^2+(\frac{y}{4}+\frac{3y}{4})\frac{4x}{5}+\frac{y}{4}\times \frac{3y}{4}$ [using the identity, $(x+a)(x+b)=x^2+(a+b)x+ab$]
$=\frac{16}{25}{x}^2+\frac{4xy}{5}+\frac{3y^2}{16}$