Precalculus Examples

$4 \sin^{2} (x) - 9 \cos^{2} (x)$

Step 1

Rewrite $4 \sin^{2} (x)$ as ${(2 \sin (x))}^{2}$ .

${(2 \sin (x))}^{2} - 9 \cos^{2} (x)$

Step 2

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

${(2 \sin (x))}^{2} - {(3 \cos (x))}^{2}$

Step 3

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

$(2 \sin (x) + 3 \cos (x)) (2 \sin (x) - (3 \cos (x)))$

Step 4

Multiply $3$ by $- 1$ .

$(2 \sin (x) + 3 \cos (x)) (2 \sin (x) - 3 \cos (x))$