Question

The value of ${(5x-3y)}^2-{(5x+3y)}^2$, when $x=-1$ and $y=\sqrt{\frac{1}{25}}$ is

• A. $12$
• B. $\frac{1}{15}$
• C. $10$
• D. $-30$

Answer 1

The correct option is A $12$

We know, $(a-b{)}^2-(a+b{)}^2=(a^2-2ab+b^2)-(a^2+2ab+b^2)$
$\Rightarrow (a-b{)}^2-(a+b{)}^2=-4ab$
On putting $a=5x$ and $b=3y$, we get
$\Rightarrow (5x-3y{)}^2-(5x+3y{)}^2=-4\left(5x\right)\left(3y\right)=-60xy$
When $x=-1$ and $y=\sqrt{\frac{1}{25}}=\frac{1}{5}$
$\Rightarrow (5x-3y{)}^2-(5x+3y{)}^2=-60(-1)\left(\frac{1}{5}\right)=12$