Algebra Examples

$- 2 (3 m^{3} + 5 m + 6) + 3 m (2 m^{2} + 3 m + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 (3 m^{3}) - 2 (5 m) - 2 \cdot 6 + 3 m (2 m^{2} + 3 m + 1)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $- 2$ .

$- 6 m^{3} - 2 (5 m) - 2 \cdot 6 + 3 m (2 m^{2} + 3 m + 1)$

Step 1.2.2

Multiply $5$ by $- 2$ .

$- 6 m^{3} - 10 m - 2 \cdot 6 + 3 m (2 m^{2} + 3 m + 1)$

Step 1.2.3

Multiply $- 2$ by $6$ .

$- 6 m^{3} - 10 m - 12 + 3 m (2 m^{2} + 3 m + 1)$

Step 1.3

Apply the distributive property.

$- 6 m^{3} - 10 m - 12 + 3 m (2 m^{2}) + 3 m (3 m) + 3 m \cdot 1$

Step 1.4

Simplify.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 m \cdot m^{2} + 3 m (3 m) + 3 m \cdot 1$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 m \cdot m^{2} + 3 \cdot 3 m \cdot m + 3 m \cdot 1$

Step 1.4.3

Multiply $3$ by $1$ .

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 m \cdot m^{2} + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5

Simplify each term.

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Step 1.5.1

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

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Step 1.5.1.1

Move $m^{2}$ .

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 (m^{2} m) + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5.1.2

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

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Step 1.5.1.2.1

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

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 (m^{2} m^{1}) + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5.1.2.2

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

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 m^{2 + 1} + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5.1.3

Add $2$ and $1$ .

$- 6 m^{3} - 10 m - 12 + 3 \cdot 2 m^{3} + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5.2

Multiply $3$ by $2$ .

$- 6 m^{3} - 10 m - 12 + 6 m^{3} + 3 \cdot 3 m \cdot m + 3 m$

Step 1.5.3

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

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Step 1.5.3.1

Move $m$ .

$- 6 m^{3} - 10 m - 12 + 6 m^{3} + 3 \cdot 3 (m \cdot m) + 3 m$

Step 1.5.3.2

Multiply $m$ by $m$ .

$- 6 m^{3} - 10 m - 12 + 6 m^{3} + 3 \cdot 3 m^{2} + 3 m$

Step 1.5.4

Multiply $3$ by $3$ .

$- 6 m^{3} - 10 m - 12 + 6 m^{3} + 9 m^{2} + 3 m$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $- 6 m^{3} - 10 m - 12 + 6 m^{3} + 9 m^{2} + 3 m$ .

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Step 2.1.1

Add $- 6 m^{3}$ and $6 m^{3}$ .

$- 10 m - 12 + 0 + 9 m^{2} + 3 m$

Step 2.1.2

Add $- 10 m - 12$ and $0$ .

$- 10 m - 12 + 9 m^{2} + 3 m$

Step 2.2

Add $- 10 m$ and $3 m$ .

$- 7 m - 12 + 9 m^{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $- 12$ .

$- 7 m + 9 m^{2} - 12$

Step 2.3.2

Reorder $- 7 m$ and $9 m^{2}$ .

$9 m^{2} - 7 m - 12$