Basic Math Examples

$p^{3} - 4 p^{2} - 55 p + 91 \div (p - 9)$

Step 1

Rewrite the division as a fraction.

$p^{3} - 4 p^{2} - 55 p + \frac{91}{p - 9}$

Step 2

To write $p^{3}$ as a fraction with a common denominator, multiply by $\frac{p - 9}{p - 9}$ .

$- 4 p^{2} - 55 p + \frac{p^{3} (p - 9)}{p - 9} + \frac{91}{p - 9}$

Step 3

Combine the numerators over the common denominator.

$- 4 p^{2} - 55 p + \frac{p^{3} (p - 9) + 91}{p - 9}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$- 4 p^{2} - 55 p + \frac{p^{3} p + p^{3} \cdot - 9 + 91}{p - 9}$

Step 4.2

Multiply $p^{3}$ by $p$ by adding the exponents.

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Step 4.2.1

Multiply $p^{3}$ by $p$ .

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Step 4.2.1.1

Raise $p$ to the power of $1$ .

$- 4 p^{2} - 55 p + \frac{p^{3} p^{1} + p^{3} \cdot - 9 + 91}{p - 9}$

Step 4.2.1.2

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

$- 4 p^{2} - 55 p + \frac{p^{3 + 1} + p^{3} \cdot - 9 + 91}{p - 9}$

Step 4.2.2

Add $3$ and $1$ .

$- 4 p^{2} - 55 p + \frac{p^{4} + p^{3} \cdot - 9 + 91}{p - 9}$

Step 4.3

Move $- 9$ to the left of $p^{3}$ .

$- 4 p^{2} - 55 p + \frac{p^{4} - 9 p^{3} + 91}{p - 9}$

Step 5

To write $- 4 p^{2}$ as a fraction with a common denominator, multiply by $\frac{p - 9}{p - 9}$ .

$- 55 p - 4 p^{2} \cdot \frac{p - 9}{p - 9} + \frac{p^{4} - 9 p^{3} + 91}{p - 9}$

Step 6

Simplify terms.

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Step 6.1

Combine $- 4 p^{2}$ and $\frac{p - 9}{p - 9}$ .

$- 55 p + \frac{- 4 p^{2} (p - 9)}{p - 9} + \frac{p^{4} - 9 p^{3} + 91}{p - 9}$

Step 6.2

Combine the numerators over the common denominator.

$- 55 p + \frac{- 4 p^{2} (p - 9) + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$- 55 p + \frac{- 4 p^{2} p - 4 p^{2} \cdot - 9 + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.2

Multiply $p^{2}$ by $p$ by adding the exponents.

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Step 7.2.1

Move $p$ .

$- 55 p + \frac{- 4 (p \cdot p^{2}) - 4 p^{2} \cdot - 9 + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.2.2

Multiply $p$ by $p^{2}$ .

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Step 7.2.2.1

Raise $p$ to the power of $1$ .

$- 55 p + \frac{- 4 (p^{1} p^{2}) - 4 p^{2} \cdot - 9 + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.2.2.2

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

$- 55 p + \frac{- 4 p^{1 + 2} - 4 p^{2} \cdot - 9 + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.2.3

Add $1$ and $2$ .

$- 55 p + \frac{- 4 p^{3} - 4 p^{2} \cdot - 9 + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.3

Multiply $- 9$ by $- 4$ .

$- 55 p + \frac{- 4 p^{3} + 36 p^{2} + p^{4} - 9 p^{3} + 91}{p - 9}$

Step 7.4

Subtract $9 p^{3}$ from $- 4 p^{3}$ .

$- 55 p + \frac{- 13 p^{3} + 36 p^{2} + p^{4} + 91}{p - 9}$

Step 7.5

Reorder terms.

$- 55 p + \frac{p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 8

To write $- 55 p$ as a fraction with a common denominator, multiply by $\frac{p - 9}{p - 9}$ .

$- 55 p \cdot \frac{p - 9}{p - 9} + \frac{p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 9

Simplify terms.

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Step 9.1

Combine $- 55 p$ and $\frac{p - 9}{p - 9}$ .

$\frac{- 55 p (p - 9)}{p - 9} + \frac{p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 9.2

Combine the numerators over the common denominator.

$\frac{- 55 p (p - 9) + p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 10

Simplify the numerator.

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Step 10.1

Apply the distributive property.

$\frac{- 55 p \cdot p - 55 p \cdot - 9 + p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 10.2

Multiply $p$ by $p$ by adding the exponents.

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Step 10.2.1

Move $p$ .

$\frac{- 55 (p \cdot p) - 55 p \cdot - 9 + p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 10.2.2

Multiply $p$ by $p$ .

$\frac{- 55 p^{2} - 55 p \cdot - 9 + p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 10.3

Multiply $- 9$ by $- 55$ .

$\frac{- 55 p^{2} + 495 p + p^{4} - 13 p^{3} + 36 p^{2} + 91}{p - 9}$

Step 10.4

Add $- 55 p^{2}$ and $36 p^{2}$ .

$\frac{495 p + p^{4} - 13 p^{3} - 19 p^{2} + 91}{p - 9}$

Step 10.5

Reorder terms.

$\frac{p^{4} - 13 p^{3} - 19 p^{2} + 495 p + 91}{p - 9}$