Trigonometry Examples

$f (x) = - 9 x^{4} + 255^{2}$

Step 1

Rewrite $9 x^{4}$ as ${(3 x^{2})}^{2}$ .

$f (x) = - {(3 x^{2})}^{2} + 255^{2}$

Step 2

Reorder $- {(3 x^{2})}^{2}$ and $255^{2}$ .

$f (x) = 255^{2} - {(3 x^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 255$ and $b = 3 x^{2}$ .

$f (x) = (255 + 3 x^{2}) (255 - (3 x^{2}))$

Step 4

Simplify.

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Step 4.1

Factor $3$ out of $255 + 3 x^{2}$ .

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Step 4.1.1

Factor $3$ out of $255$ .

$f (x) = (3 \cdot 85 + 3 x^{2}) (255 - (3 x^{2}))$

Step 4.1.2

Factor $3$ out of $3 \cdot 85 + 3 x^{2}$ .

$f (x) = 3 (85 + x^{2}) (255 - (3 x^{2}))$

Step 4.2

Multiply $3$ by $- 1$ .

$f (x) = 3 (85 + x^{2}) (255 - 3 x^{2})$