Expand the Trigonometric Expression (9x^2-y^2)/(21x+7y)

$\frac{9 x^{2} - y^{2}}{21 x + 7 y}$

Step 1

Simplify the numerator.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$\frac{{(3 x)}^{2} - y^{2}}{21 x + 7 y}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 x$ and $b = y$ .

$\frac{(3 x + y) (3 x - y)}{21 x + 7 y}$

Step 2

Simplify terms.

Factor $7$ out of $21 x + 7 y$ .

Factor $7$ out of $21 x$ .

$\frac{(3 x + y) (3 x - y)}{7 (3 x) + 7 y}$

Factor $7$ out of $7 y$ .

$\frac{(3 x + y) (3 x - y)}{7 (3 x) + 7 (y)}$

Factor $7$ out of $7 (3 x) + 7 (y)$ .

$\frac{(3 x + y) (3 x - y)}{7 (3 x + y)}$

Cancel the common factor of $3 x + y$ .

Cancel the common factor.

$\frac{(3 x + y) (3 x - y)}{7 (3 x + y)}$

Rewrite the expression.

$\frac{3 x - y}{7}$