Algebra Examples

$(2 \cos (θ) - 1) (2 \cos (θ) + 1)$

Step 1

Expand $(2 \cos (θ) - 1) (2 \cos (θ) + 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$2 \cos (θ) (2 \cos (θ) + 1) - 1 (2 \cos (θ) + 1)$

Step 1.2

Apply the distributive property.

$2 \cos (θ) (2 \cos (θ)) + 2 \cos (θ) \cdot 1 - 1 (2 \cos (θ) + 1)$

Step 1.3

Apply the distributive property.

$2 \cos (θ) (2 \cos (θ)) + 2 \cos (θ) \cdot 1 - 1 (2 \cos (θ)) - 1 \cdot 1$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $2 \cos (θ) (2 \cos (θ)) + 2 \cos (θ) \cdot 1 - 1 (2 \cos (θ)) - 1 \cdot 1$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $2 \cos (θ) \cdot 1$ and $- 1 (2 \cos (θ))$ .

$2 \cos (θ) (2 \cos (θ)) + 1 \cdot 2 \cos (θ) - 1 \cdot 2 \cos (θ) - 1 \cdot 1$

Step 2.1.2

Subtract $2 \cos (θ)$ from $1 \cdot 2 \cos (θ)$ .

$2 \cos (θ) (2 \cos (θ)) + 0 - 1 \cdot 1$

Step 2.1.3

Add $2 \cos (θ) (2 \cos (θ))$ and $0$ .

$2 \cos (θ) (2 \cos (θ)) - 1 \cdot 1$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $2 \cos (θ) (2 \cos (θ))$ .

Tap for more steps...

Step 2.2.1.1

Multiply $2$ by $2$ .

$4 \cos (θ) \cos (θ) - 1 \cdot 1$

Step 2.2.1.2

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

$4 (\cos^{1} (θ) \cos (θ)) - 1 \cdot 1$

Step 2.2.1.3

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

$4 (\cos^{1} (θ) \cos^{1} (θ)) - 1 \cdot 1$

Step 2.2.1.4

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

$4 {\cos (θ)}^{1 + 1} - 1 \cdot 1$

Step 2.2.1.5

Add $1$ and $1$ .

$4 \cos^{2} (θ) - 1 \cdot 1$

Step 2.2.2

Multiply $- 1$ by $1$ .

$4 \cos^{2} (θ) - 1$