Basic Math Examples

$- 5 m (2 m^{3} - 7 m^{2} + m)$

Step 1

Apply the distributive property.

$- 5 m (2 m^{3}) - 5 m (- 7 m^{2}) - 5 m \cdot m$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 5 \cdot 2 m \cdot m^{3} - 5 m (- 7 m^{2}) - 5 m \cdot m$

Step 2.2

Rewrite using the commutative property of multiplication.

$- 5 \cdot 2 m \cdot m^{3} - 5 \cdot - 7 m \cdot m^{2} - 5 m \cdot m$

Step 2.3

Multiply $m$ by $m$ by adding the exponents.

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Step 2.3.1

Move $m$ .

$- 5 \cdot 2 m \cdot m^{3} - 5 \cdot - 7 m \cdot m^{2} - 5 (m \cdot m)$

Step 2.3.2

Multiply $m$ by $m$ .

$- 5 \cdot 2 m \cdot m^{3} - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $m^{3}$ .

$- 5 \cdot 2 (m^{3} m) - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3.1.2

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

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Step 3.1.2.1

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

$- 5 \cdot 2 (m^{3} m^{1}) - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3.1.2.2

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

$- 5 \cdot 2 m^{3 + 1} - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3.1.3

Add $3$ and $1$ .

$- 5 \cdot 2 m^{4} - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3.2

Multiply $- 5$ by $2$ .

$- 10 m^{4} - 5 \cdot - 7 m \cdot m^{2} - 5 m^{2}$

Step 3.3

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

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Step 3.3.1

Move $m^{2}$ .

$- 10 m^{4} - 5 \cdot - 7 (m^{2} m) - 5 m^{2}$

Step 3.3.2

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

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Step 3.3.2.1

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

$- 10 m^{4} - 5 \cdot - 7 (m^{2} m^{1}) - 5 m^{2}$

Step 3.3.2.2

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

$- 10 m^{4} - 5 \cdot - 7 m^{2 + 1} - 5 m^{2}$

Step 3.3.3

Add $2$ and $1$ .

$- 10 m^{4} - 5 \cdot - 7 m^{3} - 5 m^{2}$

Step 3.4

Multiply $- 5$ by $- 7$ .

$- 10 m^{4} + 35 m^{3} - 5 m^{2}$