Pre-Algebra Examples

$(18 r^{5} + 36 r^{4} + 27 r^{3}) \div 9 r$

Step 1

Rewrite the division as a fraction.

$\frac{18 r^{5} + 36 r^{4} + 27 r^{3}}{9 r}$

Step 2

Factor $9 r^{3}$ out of $18 r^{5} + 36 r^{4} + 27 r^{3}$ .

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Step 2.1

Factor $9 r^{3}$ out of $18 r^{5}$ .

$\frac{9 r^{3} (2 r^{2}) + 36 r^{4} + 27 r^{3}}{9 r}$

Step 2.2

Factor $9 r^{3}$ out of $36 r^{4}$ .

$\frac{9 r^{3} (2 r^{2}) + 9 r^{3} (4 r) + 27 r^{3}}{9 r}$

Step 2.3

Factor $9 r^{3}$ out of $27 r^{3}$ .

$\frac{9 r^{3} (2 r^{2}) + 9 r^{3} (4 r) + 9 r^{3} (3)}{9 r}$

Step 2.4

Factor $9 r^{3}$ out of $9 r^{3} (2 r^{2}) + 9 r^{3} (4 r)$ .

$\frac{9 r^{3} (2 r^{2} + 4 r) + 9 r^{3} (3)}{9 r}$

Step 2.5

Factor $9 r^{3}$ out of $9 r^{3} (2 r^{2} + 4 r) + 9 r^{3} (3)$ .

$\frac{9 r^{3} (2 r^{2} + 4 r + 3)}{9 r}$

Step 3

Cancel the common factor of $9$ .

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Step 3.1

Cancel the common factor.

$\frac{9 r^{3} (2 r^{2} + 4 r + 3)}{9 r}$

Step 3.2

Rewrite the expression.

$\frac{r^{3} (2 r^{2} + 4 r + 3)}{r}$

Step 4

Cancel the common factor of $r^{3}$ and $r$ .

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Step 4.1

Factor $r$ out of $r^{3} (2 r^{2} + 4 r + 3)$ .

$\frac{r (r^{2} (2 r^{2} + 4 r + 3))}{r}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{r (r^{2} (2 r^{2} + 4 r + 3))}{r^{1}}$

Step 4.2.2

Factor $r$ out of $r^{1}$ .

$\frac{r (r^{2} (2 r^{2} + 4 r + 3))}{r \cdot 1}$

Step 4.2.3

Cancel the common factor.

$\frac{r (r^{2} (2 r^{2} + 4 r + 3))}{r \cdot 1}$

Step 4.2.4

Rewrite the expression.

$\frac{r^{2} (2 r^{2} + 4 r + 3)}{1}$

Step 4.2.5

Divide $r^{2} (2 r^{2} + 4 r + 3)$ by $1$ .

$r^{2} (2 r^{2} + 4 r + 3)$

Step 5

Apply the distributive property.

$r^{2} (2 r^{2}) + r^{2} (4 r) + r^{2} \cdot 3$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$2 r^{2} r^{2} + r^{2} (4 r) + r^{2} \cdot 3$

Step 6.2

Rewrite using the commutative property of multiplication.

$2 r^{2} r^{2} + 4 r^{2} r + r^{2} \cdot 3$

Step 6.3

Move $3$ to the left of $r^{2}$ .

$2 r^{2} r^{2} + 4 r^{2} r + 3 \cdot r^{2}$

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

Move $r^{2}$ .

$2 (r^{2} r^{2}) + 4 r^{2} r + 3 \cdot r^{2}$

Step 7.1.2

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

$2 r^{2 + 2} + 4 r^{2} r + 3 \cdot r^{2}$

Step 7.1.3

Add $2$ and $2$ .

$2 r^{4} + 4 r^{2} r + 3 \cdot r^{2}$

Step 7.2

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

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Step 7.2.1

Move $r$ .

$2 r^{4} + 4 (r \cdot r^{2}) + 3 \cdot r^{2}$

Step 7.2.2

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

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Step 7.2.2.1

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

$2 r^{4} + 4 (r^{1} r^{2}) + 3 \cdot r^{2}$

Step 7.2.2.2

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

$2 r^{4} + 4 r^{1 + 2} + 3 \cdot r^{2}$

Step 7.2.3

Add $1$ and $2$ .

$2 r^{4} + 4 r^{3} + 3 \cdot r^{2}$

$2 r^{4} + 4 r^{3} + 3 r^{2}$