Trigonometry Examples

$f (x) = {(x^{2} - 25)}^{5}$

Step 1

Rewrite $25$ as $5^{2}$ .

$f (x) = {(x^{2} - 5^{2})}^{5}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$f (x) = {((x + 5) (x - 5))}^{5}$

Step 3

Apply the product rule to $(x + 5) (x - 5)$ .

$f (x) = {(x + 5)}^{5} {(x - 5)}^{5}$