Question

Use a suitable identity to get each of the following products:
$(\frac{x}{2}+\frac{3y}{4})(\frac{x}{2}+\frac{3y}{4})$

• A. $\frac{x^2}{4}+\frac{3}{16}xy+\frac{3}{4}{y}^2$
• B. $\frac{x^2}{4}+\frac{3}{2}xy+\frac{9}{16}{y}^2$
• C. $\frac{x^2}{4}+\frac{3}{4}xy+\frac{9}{16}{y}^2$
• D. $\frac{x^2}{2}+\frac{3}{2}xy+\frac{9}{8}{y}^2$

Answer 1

The correct option is C

$\frac{x^2}{4}+\frac{3}{4}xy+\frac{9}{16}{y}^2$

$(\frac{x}{2}+\frac{3y}{4})(\frac{x}{2}+\frac{3y}{4})={(\frac{x}{2}+\frac{3y}{4})}^2$
$={\left(\frac{x}{2}\right)}^2+2\times \frac{x}{2}\times \frac{3y}{4}+{\left(\frac{3y}{4}\right)}^2\left[\text{Using Identity}\right(a+b{)}^2=a^2+2ab+b^2]$
$=\frac{x^2}{4}+\frac{3}{4}xy+\frac{9}{16}{y}^2$