Trigonometry Examples

$(\cos (x) + 1) (3 \cos (x) - 1)$

Step 1

Expand $(\cos (x) + 1) (3 \cos (x) - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\cos (x) (3 \cos (x) - 1) + 1 (3 \cos (x) - 1)$

Step 1.2

Apply the distributive property.

$\cos (x) (3 \cos (x)) + \cos (x) \cdot - 1 + 1 (3 \cos (x) - 1)$

Step 1.3

Apply the distributive property.

$\cos (x) (3 \cos (x)) + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$3 \cos (x) \cos (x) + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.2

Multiply $3 \cos (x) \cos (x)$ .

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Step 2.1.2.1

Raise $\cos (x)$ to the power of $1$ .

$3 (\cos^{1} (x) \cos (x)) + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.2.2

Raise $\cos (x)$ to the power of $1$ .

$3 (\cos^{1} (x) \cos^{1} (x)) + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.2.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 {\cos (x)}^{1 + 1} + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.2.4

Add $1$ and $1$ .

$3 \cos^{2} (x) + \cos (x) \cdot - 1 + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.3

Move $- 1$ to the left of $\cos (x)$ .

$3 \cos^{2} (x) - 1 \cdot \cos (x) + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.4

Rewrite $- 1 \cos (x)$ as $- \cos (x)$ .

$3 \cos^{2} (x) - \cos (x) + 1 (3 \cos (x)) + 1 \cdot - 1$

Step 2.1.5

Multiply $3 \cos (x)$ by $1$ .

$3 \cos^{2} (x) - \cos (x) + 3 \cos (x) + 1 \cdot - 1$

Step 2.1.6

Multiply $- 1$ by $1$ .

$3 \cos^{2} (x) - \cos (x) + 3 \cos (x) - 1$

Step 2.2

Add $- \cos (x)$ and $3 \cos (x)$ .

$3 \cos^{2} (x) + 2 \cos (x) - 1$

Step 3

The polynomial cannot be factored using the specified method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the specified method.