Pre-Algebra Examples

$(20 m^{9} - 20 m^{8} - 4 m^{5}) \div 2 m^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{20 m^{9} - 20 m^{8} - 4 m^{5}}{2 m^{3}}$

Step 2

Factor $4 m^{5}$ out of $20 m^{9} - 20 m^{8} - 4 m^{5}$ .

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Step 2.1

Factor $4 m^{5}$ out of $20 m^{9}$ .

$\frac{4 m^{5} (5 m^{4}) - 20 m^{8} - 4 m^{5}}{2 m^{3}}$

Step 2.2

Factor $4 m^{5}$ out of $- 20 m^{8}$ .

$\frac{4 m^{5} (5 m^{4}) + 4 m^{5} (- 5 m^{3}) - 4 m^{5}}{2 m^{3}}$

Step 2.3

Factor $4 m^{5}$ out of $- 4 m^{5}$ .

$\frac{4 m^{5} (5 m^{4}) + 4 m^{5} (- 5 m^{3}) + 4 m^{5} (- 1)}{2 m^{3}}$

Step 2.4

Factor $4 m^{5}$ out of $4 m^{5} (5 m^{4}) + 4 m^{5} (- 5 m^{3})$ .

$\frac{4 m^{5} (5 m^{4} - 5 m^{3}) + 4 m^{5} (- 1)}{2 m^{3}}$

Step 2.5

Factor $4 m^{5}$ out of $4 m^{5} (5 m^{4} - 5 m^{3}) + 4 m^{5} (- 1)$ .

$\frac{4 m^{5} (5 m^{4} - 5 m^{3} - 1)}{2 m^{3}}$

Step 3

Cancel the common factor of $4$ and $2$ .

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Step 3.1

Factor $2$ out of $4 m^{5} (5 m^{4} - 5 m^{3} - 1)$ .

$\frac{2 (2 m^{5} (5 m^{4} - 5 m^{3} - 1))}{2 m^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 m^{3}$ .

$\frac{2 (2 m^{5} (5 m^{4} - 5 m^{3} - 1))}{2 (m^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (2 m^{5} (5 m^{4} - 5 m^{3} - 1))}{2 m^{3}}$

Step 3.2.3

Rewrite the expression.

$\frac{2 m^{5} (5 m^{4} - 5 m^{3} - 1)}{m^{3}}$

Step 4

Cancel the common factor of $m^{5}$ and $m^{3}$ .

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Step 4.1

Factor $m^{3}$ out of $2 m^{5} (5 m^{4} - 5 m^{3} - 1)$ .

$\frac{m^{3} (2 m^{2} (5 m^{4} - 5 m^{3} - 1))}{m^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{m^{3} (2 m^{2} (5 m^{4} - 5 m^{3} - 1))}{m^{3} \cdot 1}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{3} (2 m^{2} (5 m^{4} - 5 m^{3} - 1))}{m^{3} \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{2 m^{2} (5 m^{4} - 5 m^{3} - 1)}{1}$

Step 4.2.4

Divide $2 m^{2} (5 m^{4} - 5 m^{3} - 1)$ by $1$ .

$2 m^{2} (5 m^{4} - 5 m^{3} - 1)$

Step 5

Apply the distributive property.

$2 m^{2} (5 m^{4}) + 2 m^{2} (- 5 m^{3}) + 2 m^{2} \cdot - 1$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 m^{2} m^{4} + 2 m^{2} (- 5 m^{3}) + 2 m^{2} \cdot - 1$

Step 6.2

Rewrite using the commutative property of multiplication.

$2 \cdot 5 m^{2} m^{4} + 2 \cdot - 5 m^{2} m^{3} + 2 m^{2} \cdot - 1$

Step 6.3

Multiply $- 1$ by $2$ .

$2 \cdot 5 m^{2} m^{4} + 2 \cdot - 5 m^{2} m^{3} - 2 m^{2}$

Step 7

Simplify each term.

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Step 7.1

Multiply $m^{2}$ by $m^{4}$ by adding the exponents.

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Step 7.1.1

Move $m^{4}$ .

$2 \cdot 5 (m^{4} m^{2}) + 2 \cdot - 5 m^{2} m^{3} - 2 m^{2}$

Step 7.1.2

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

$2 \cdot 5 m^{4 + 2} + 2 \cdot - 5 m^{2} m^{3} - 2 m^{2}$

Step 7.1.3

Add $4$ and $2$ .

$2 \cdot 5 m^{6} + 2 \cdot - 5 m^{2} m^{3} - 2 m^{2}$

Step 7.2

Multiply $2$ by $5$ .

$10 m^{6} + 2 \cdot - 5 m^{2} m^{3} - 2 m^{2}$

Step 7.3

Multiply $m^{2}$ by $m^{3}$ by adding the exponents.

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Step 7.3.1

Move $m^{3}$ .

$10 m^{6} + 2 \cdot - 5 (m^{3} m^{2}) - 2 m^{2}$

Step 7.3.2

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

$10 m^{6} + 2 \cdot - 5 m^{3 + 2} - 2 m^{2}$

Step 7.3.3

Add $3$ and $2$ .

$10 m^{6} + 2 \cdot - 5 m^{5} - 2 m^{2}$

Step 7.4

Multiply $2$ by $- 5$ .

$10 m^{6} - 10 m^{5} - 2 m^{2}$