Algebra Examples

$(8 m^{7} - 10 m^{5}) \div 2 m^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{8 m^{7} - 10 m^{5}}{2 m^{3}}$

Step 2

Factor $2 m^{5}$ out of $8 m^{7} - 10 m^{5}$ .

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Step 2.1

Factor $2 m^{5}$ out of $8 m^{7}$ .

$\frac{2 m^{5} (4 m^{2}) - 10 m^{5}}{2 m^{3}}$

Step 2.2

Factor $2 m^{5}$ out of $- 10 m^{5}$ .

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

Step 2.3

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

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

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.2.4

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

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

Step 5

Apply the distributive property.

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

Move $- 5$ to the left of $m^{2}$ .

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

Step 8

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

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Step 8.1

Move $m^{2}$ .

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

Step 8.2

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

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

Step 8.3

Add $2$ and $2$ .

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

$4 m^{4} - 5 m^{2}$