Question

State whether the statement is True or False:

${(2a-\frac{1}{a})}^2$ is equal to $4a^2-4+\frac{1}{a^2}$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, $(2a-\frac{1}{a}{)}^2$.

We know, $(x-y{)}^2=x^2-2xy+y^2$.

Then,

$(2a-\frac{1}{a}{)}^2={\left(2a\right)}^2-2(2a\left)\right(\frac{1}{a})+(\frac{1}{a}{)}^2=4a^2-4+\frac{1}{a^2}.$

Therefore, the statement is true.

Hence, option $A$ is correct.