Question

Evaluate: ${(\frac{a}{2b}+\frac{2b}{a})}^2-{(\frac{a}{2b}-\frac{2b}{a})}^2-4$.

• A. $0$
• B. $1$
• C. $3$
• D. $6$

Answer 1

The correct option is A $0$

Given, ${(\frac{a}{2b}+\frac{2b}{a})}^2-{(\frac{a}{2b}-\frac{2b}{a})}^2-4$.

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

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

Then,

${(\frac{a}{2b}+\frac{2b}{a})}^2-{(\frac{a}{2b}-\frac{2b}{a})}^2-4$

$=\left[\right(\frac{a}{2b}{)}^2+(\frac{2b}{a}{)}^2+2(\frac{a}{2b}\left)\right(\frac{2b}{a}\left)\right]-\left[\right(\frac{a}{2b}{)}^2+(\frac{2b}{a}{)}^2-2(\frac{a}{2b}\left)\right(\frac{2b}{a}\left)\right]-4$

$=(\frac{a}{2b}{)}^2+(\frac{2b}{a}{)}^2+2-(\frac{a}{2b}{)}^2-(\frac{2b}{a}{)}^2+2-4$

$=0$.

Therefore, option $A$ is correct.