Question

The factors of $\frac{x^2}{4}-\frac{y^2}{9}$ are ______.

• A. $(\frac{x}{4}+\frac{y}{9})(\frac{x}{4}-\frac{y}{9})$
• B. $(\frac{x}{2}+\frac{y}{9})(\frac{x}{2}-\frac{y}{9})$
• C. $(\frac{x}{2}+\frac{y}{3})(\frac{x}{2}-\frac{y}{3})$
• D. Both $\left(A\right)$ and $\left(B\right)$

Answer 1

The correct option is C $(\frac{x}{2}+\frac{y}{3})(\frac{x}{2}-\frac{y}{3})$

We know that, $a^2-b^2=(a+b)(a-b)$ .....$(\because \text{Identity})$

Given, $\frac{x^2}{4}-\frac{y^2}{9}$

Here, $a=\frac{x}{2}$ and $b=\frac{y}{3}$

Thus $\frac{x^2}{4}-\frac{y^2}{9}=(\frac{x}{2}+\frac{y}{3})(\frac{x}{2}-\frac{y}{3})$