Simplify -2(3m^3+5m+6)+3m(2m^2+3m+1)

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

Step 1

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $3$ by $- 2$ .

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

Multiply $5$ by $- 2$ .

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

Multiply $- 2$ by $6$ .

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $1$ .

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

Simplify each term.

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

Move $m^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $2$ .

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

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

Move $m$ .

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

Multiply $m$ by $m$ .

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

Multiply $3$ by $3$ .

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

Step 2

Simplify by adding terms.

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

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

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

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

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

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

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

Simplify the expression.

Move $- 12$ .

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

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

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

Simplify -2(3m^3+5m+6)+3m(2m^2+3m+1)

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