Question

State whether the statement is True or False:

The square of $(2m^2-\frac{2}{3}{n}^2)$ is equal to $4m^4-\frac{8}{3}{m}^2{n}^2+\frac{4}{9}{n}^4$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, square of $(2m^2-\frac{2}{3}{n}^2)$,

i.e. $(2m^2-\frac{2}{3}{n}^2{)}^2$.

We know. $(a-b{)}^2=a^2-2ab+b^2$.

Then,

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

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

$=4m^4+\frac{4}{9}{n}^4-\frac{8}{3}{m}^2{n}^2$.

Here, the statement is true.

Therefore, option $A$ is correct.