Rewriting a Trigonometric Expression Using the Difference of Squares

Rewrite the trigonometric expression: $4 \cos^{2} θ - 1.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Notice that both the coefficient and the trigonometric expression in the first term are squared, and the square of the number 1 is 1. This is the difference of squares. Thus,

$\begin{array}{l} 4 \cos^{2} θ - 1 = {(2 \cos θ)}^{2} - 1 \\ = (2 \cos θ - 1) (2 \cos θ + 1) \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Rewrite the trigonometric expression: $25 - 9 \sin^{2} θ .$

How did it go?