Question

Find the square by using the identities.

${(\frac{2}{3}m+\frac{3}{2}n)}^2$

• A. $\frac{4}{9}{m}^2+2mn+\frac{9}{4}{n}^2$
• B. $\frac{1}{49}{m}^2+2n+\frac{9}{4}{n}^2$
• C. $\frac{4}{7}{m}^2+2m+\frac{9}{4}{m}^2$
• D. $\frac{3}{2}{n}^2+2mn+\frac{9}{4}{m}^7$

Answer 1

The correct option is A $\frac{4}{9}{m}^2+2mn+\frac{9}{4}{n}^2$

Given, ${(\frac{2}{3}m+\frac{3}{2}n)}^2$

Using $(a+b{)}^2=a^2+2ab+b^2$ we get,

$={\left(\frac{2}{3}m\right)}^2+2\left[\left(\frac{2}{3}m\right)\left(\frac{3}{2}n\right)\right]+{\left(\frac{3}{2}n\right)}^2$

$=\left(\frac{4}{9}{m}^2\right)+2mn+\left(\frac{9}{4}{n}^2\right)$