Finite Math Examples

$2 r \cos (α) + {(r \cos (α))}^{2} \cdot \cos (α)$

Step 1

Factor

$\cos (α)$ out of

$2 r \cos (α) + {(r \cos (α))}^{2} \cdot \cos (α)$ .

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Step 1.1

Factor

$\cos (α)$ out of

$2 r \cos (α)$ .

$\cos (α) (2 r) + {(r \cos (α))}^{2} \cdot \cos (α)$

Step 1.2

Factor

$\cos (α)$ out of

${(r \cos (α))}^{2} \cdot \cos (α)$ .

$\cos (α) (2 r) + \cos (α) \cdot {(r \cos (α))}^{2}$

Step 1.3

Factor

$\cos (α)$ out of

$\cos (α) (2 r) + \cos (α) \cdot {(r \cos (α))}^{2}$ .

$\cos (α) (2 r + {(r \cos (α))}^{2})$

Step 2

Let

$u = r$ . Substitute

$u$ for all occurrences of

$r$ .

$\cos (α) (2 u + u^{2} \cos^{2} (α))$

Step 3

Factor

$u$ out of

$2 u + u^{2} \cos^{2} (α)$ .

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Step 3.1

Factor

$u$ out of

$2 u$ .

$\cos (α) (u \cdot 2 + u^{2} \cos^{2} (α))$

Step 3.2

Factor

$u$ out of

$u^{2} \cos^{2} (α)$ .

$\cos (α) (u \cdot 2 + u (u \cos^{2} (α)))$

Step 3.3

Factor

$u$ out of

$u \cdot 2 + u (u \cos^{2} (α))$ .

$\cos (α) (u (2 + u \cos^{2} (α)))$

Step 4

Factor.

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Step 4.1

Replace all occurrences of

$u$ with

$r$ .

$\cos (α) (r (2 + r \cos^{2} (α)))$

Step 4.2

Remove unnecessary parentheses.

$\cos (α) r (2 + r \cos^{2} (α))$

Step 5

Apply the distributive property.

$\cos (α) r \cdot 2 + \cos (α) r (r \cos^{2} (α))$

Step 6

Move

$2$ to the left of

$\cos (α) r$ .

$2 \cdot (\cos (α) r) + \cos (α) r (r \cos^{2} (α))$

Step 7

Multiply

$\cos (α)$ by

$\cos^{2} (α)$ by adding the exponents.

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Step 7.1

Move

$\cos^{2} (α)$ .

$2 \cdot (\cos (α) r) + \cos^{2} (α) \cos (α) r \cdot r$

Step 7.2

Multiply

$\cos^{2} (α)$ by

$\cos (α)$ .

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Step 7.2.1

Raise

$\cos (α)$ to the power of

$1$ .

$2 \cdot (\cos (α) r) + \cos^{2} (α) \cos^{1} (α) r \cdot r$

Step 7.2.2

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot (\cos (α) r) + {\cos (α)}^{2 + 1} r \cdot r$

Step 7.3

Add

$2$ and

$1$ .

$2 \cdot (\cos (α) r) + \cos^{3} (α) r \cdot r$

Step 8

Multiply

$r$ by

$r$ by adding the exponents.

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Step 8.1

Move

$r$ .

$2 \cos (α) r + \cos^{3} (α) (r \cdot r)$

Step 8.2

Multiply

$r$ by

$r$ .

$2 \cos (α) r + \cos^{3} (α) r^{2}$

Step 9

Reorder factors in

$2 \cos (α) r + \cos^{3} (α) r^{2}$ .

$2 r \cos (α) + r^{2} \cos^{3} (α)$

Step 10

Factor

$r \cos (α)$ out of

$2 r \cos (α) + r^{2} \cos^{3} (α)$ .

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Step 10.1

Factor

$r \cos (α)$ out of

$2 r \cos (α)$ .

$r \cos (α) (2) + r^{2} \cos^{3} (α)$

Step 10.2

Factor

$r \cos (α)$ out of

$r^{2} \cos^{3} (α)$ .

$r \cos (α) (2) + r \cos (α) (r \cos^{2} (α))$

Step 10.3

Factor

$r \cos (α)$ out of

$r \cos (α) (2) + r \cos (α) (r \cos^{2} (α))$ .

$r \cos (α) (2 + r \cos^{2} (α))$