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. None of these

Answer 1

Answer: (C)

$(\frac{x}{2}+\frac{y}{3})(\frac{x}{2}-\frac{y}{3})$

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