Basic Math Examples

$r^{4} + 12 r^{3} + 25 r^{2} + 48 r \cdot r - 18 \div (r + 10)$

Step 1

Simplify each term.

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Step 1.1

Multiply $r$ by $r$ by adding the exponents.

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Step 1.1.1

Move $r$ .

$r^{4} + 12 r^{3} + 25 r^{2} + 48 (r \cdot r) - 18 \div (r + 10)$

Step 1.1.2

Multiply $r$ by $r$ .

$r^{4} + 12 r^{3} + 25 r^{2} + 48 r^{2} - 18 \div (r + 10)$

Step 1.2

Rewrite the division as a fraction.

$r^{4} + 12 r^{3} + 25 r^{2} + 48 r^{2} - \frac{18}{r + 10}$

Step 2

To write $r^{4}$ as a fraction with a common denominator, multiply by $\frac{r + 10}{r + 10}$ .

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{4} (r + 10)}{r + 10} - \frac{18}{r + 10}$

Step 3

Combine the numerators over the common denominator.

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{4} (r + 10) - 18}{r + 10}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{4} r + r^{4} \cdot 10 - 18}{r + 10}$

Step 4.2

Multiply $r^{4}$ by $r$ by adding the exponents.

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Step 4.2.1

Multiply $r^{4}$ by $r$ .

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Step 4.2.1.1

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

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{4} r^{1} + r^{4} \cdot 10 - 18}{r + 10}$

Step 4.2.1.2

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

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{4 + 1} + r^{4} \cdot 10 - 18}{r + 10}$

Step 4.2.2

Add $4$ and $1$ .

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{5} + r^{4} \cdot 10 - 18}{r + 10}$

Step 4.3

Move $10$ to the left of $r^{4}$ .

$12 r^{3} + 25 r^{2} + 48 r^{2} + \frac{r^{5} + 10 r^{4} - 18}{r + 10}$

Step 5

To write $12 r^{3}$ as a fraction with a common denominator, multiply by $\frac{r + 10}{r + 10}$ .

$25 r^{2} + 48 r^{2} + \frac{12 r^{3} (r + 10)}{r + 10} + \frac{r^{5} + 10 r^{4} - 18}{r + 10}$

Step 6

Combine the numerators over the common denominator.

$25 r^{2} + 48 r^{2} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7

Find the common denominator.

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Step 7.1

Write $25 r^{2}$ as a fraction with denominator $1$ .

$\frac{25 r^{2}}{1} + 48 r^{2} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7.2

Multiply $\frac{25 r^{2}}{1}$ by $\frac{r + 10}{r + 10}$ .

$\frac{25 r^{2}}{1} \cdot \frac{r + 10}{r + 10} + 48 r^{2} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7.3

Multiply $\frac{25 r^{2}}{1}$ by $\frac{r + 10}{r + 10}$ .

$\frac{25 r^{2} (r + 10)}{r + 10} + 48 r^{2} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7.4

Write $48 r^{2}$ as a fraction with denominator $1$ .

$\frac{25 r^{2} (r + 10)}{r + 10} + \frac{48 r^{2}}{1} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7.5

Multiply $\frac{48 r^{2}}{1}$ by $\frac{r + 10}{r + 10}$ .

$\frac{25 r^{2} (r + 10)}{r + 10} + \frac{48 r^{2}}{1} \cdot \frac{r + 10}{r + 10} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 7.6

Multiply $\frac{48 r^{2}}{1}$ by $\frac{r + 10}{r + 10}$ .

$\frac{25 r^{2} (r + 10)}{r + 10} + \frac{48 r^{2} (r + 10)}{r + 10} + \frac{12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 8

Combine the numerators over the common denominator.

$\frac{25 r^{2} (r + 10) + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9

Simplify each term.

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Step 9.1

Apply the distributive property.

$\frac{25 r^{2} r + 25 r^{2} \cdot 10 + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.2

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

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Step 9.2.1

Move $r$ .

$\frac{25 (r \cdot r^{2}) + 25 r^{2} \cdot 10 + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.2.2

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

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Step 9.2.2.1

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

$\frac{25 (r^{1} r^{2}) + 25 r^{2} \cdot 10 + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.2.2.2

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

$\frac{25 r^{1 + 2} + 25 r^{2} \cdot 10 + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.2.3

Add $1$ and $2$ .

$\frac{25 r^{3} + 25 r^{2} \cdot 10 + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.3

Multiply $10$ by $25$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{2} (r + 10) + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.4

Apply the distributive property.

$\frac{25 r^{3} + 250 r^{2} + 48 r^{2} r + 48 r^{2} \cdot 10 + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.5

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

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Step 9.5.1

Move $r$ .

$\frac{25 r^{3} + 250 r^{2} + 48 (r \cdot r^{2}) + 48 r^{2} \cdot 10 + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.5.2

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

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Step 9.5.2.1

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

$\frac{25 r^{3} + 250 r^{2} + 48 (r^{1} r^{2}) + 48 r^{2} \cdot 10 + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.5.2.2

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

$\frac{25 r^{3} + 250 r^{2} + 48 r^{1 + 2} + 48 r^{2} \cdot 10 + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.5.3

Add $1$ and $2$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 48 r^{2} \cdot 10 + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.6

Multiply $10$ by $48$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 r^{3} (r + 10) + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.7

Apply the distributive property.

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 r^{3} r + 12 r^{3} \cdot 10 + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.8

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

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Step 9.8.1

Move $r$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 (r \cdot r^{3}) + 12 r^{3} \cdot 10 + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.8.2

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

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Step 9.8.2.1

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

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 (r^{1} r^{3}) + 12 r^{3} \cdot 10 + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.8.2.2

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

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 r^{1 + 3} + 12 r^{3} \cdot 10 + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.8.3

Add $1$ and $3$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 r^{4} + 12 r^{3} \cdot 10 + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 9.9

Multiply $10$ by $12$ .

$\frac{25 r^{3} + 250 r^{2} + 48 r^{3} + 480 r^{2} + 12 r^{4} + 120 r^{3} + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 10

Simplify by adding terms.

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Step 10.1

Add $25 r^{3}$ and $48 r^{3}$ .

$\frac{73 r^{3} + 250 r^{2} + 480 r^{2} + 12 r^{4} + 120 r^{3} + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 10.2

Add $73 r^{3}$ and $120 r^{3}$ .

$\frac{193 r^{3} + 250 r^{2} + 480 r^{2} + 12 r^{4} + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 10.3

Add $250 r^{2}$ and $480 r^{2}$ .

$\frac{193 r^{3} + 730 r^{2} + 12 r^{4} + r^{5} + 10 r^{4} - 18}{r + 10}$

Step 10.4

Add $12 r^{4}$ and $10 r^{4}$ .

$\frac{193 r^{3} + 730 r^{2} + r^{5} + 22 r^{4} - 18}{r + 10}$

Step 10.5

Reorder.

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Step 10.5.1

Move $730 r^{2}$ .

$\frac{193 r^{3} + r^{5} + 22 r^{4} + 730 r^{2} - 18}{r + 10}$

Step 10.5.2

Move $193 r^{3}$ .

$\frac{r^{5} + 22 r^{4} + 193 r^{3} + 730 r^{2} - 18}{r + 10}$