Calculus Examples

$(4 π - 4 x) (2 + 2 \cos (x - π))$

Step 1

Expand $(4 π - 4 x) (2 + 2 \cos (x - π))$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 π (2 + 2 \cos (x - π)) - 4 x (2 + 2 \cos (x - π))$

Step 1.2

Apply the distributive property.

$4 π \cdot 2 + 4 π (2 \cos (x - π)) - 4 x (2 + 2 \cos (x - π))$

Step 1.3

Apply the distributive property.

$4 π \cdot 2 + 4 π (2 \cos (x - π)) - 4 x \cdot 2 - 4 x (2 \cos (x - π))$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $2$ by $4$ .

$8 π + 4 π (2 \cos (x - π)) - 4 x \cdot 2 - 4 x (2 \cos (x - π))$

Step 2.1.2

Multiply $2$ by $4$ .

$8 π + 8 π \cos (x - π) - 4 x \cdot 2 - 4 x (2 \cos (x - π))$

Step 2.1.3

Multiply $2$ by $- 4$ .

$8 π + 8 π \cos (x - π) - 8 x - 4 x (2 \cos (x - π))$

Step 2.1.4

Multiply $2$ by $- 4$ .

$8 π + 8 π \cos (x - π) - 8 x - 8 x \cos (x - π)$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $8 π \cos (x - π)$ .

$8 π - 8 x + 8 π \cos (x - π) - 8 x \cos (x - π)$

Step 2.2.2

Reorder $8 π$ and $- 8 x$ .

$- 8 x + 8 π + 8 π \cos (x - π) - 8 x \cos (x - π)$