Question

State whether the statement is True or False:

The square of $(3x+\frac{2}{y})$ is equal to $9x^2+\frac{12x}{y}+\frac{4}{y^2}$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, square of $(3x+\frac{2}{y})$,

i.e. $(3x+\frac{2}{y}{)}^2$.

Applying the formula $(a+b{)}^2=a^2+2ab+b^2$, where $a=3x,b=\frac{2}{y}$.

$(3x+\frac{2}{y}{)}^2$
$=(3x{)}^2+2(3x\left)\right(\frac{2}{y})+(\frac{2}{y}{)}^2$
$=9x^2+12\frac{x}{y}+\frac{4}{y^2}$
$=9x^2+\frac{12x}{y}+\frac{4}{y^2}$.

Hence, the statement is true.

Therefore, option $A$ is correct.