Simplify (m+2)((m^2+3m-6)+(m^2-2m+4))

$(m + 2) ((m^{2} + 3 m - 6) + (m^{2} - 2 m + 4))$

Step 1

Simplify by adding terms.

Remove parentheses.

$(m + 2) (m^{2} + 3 m - 6 + m^{2} - 2 m + 4)$

Add $m^{2}$ and $m^{2}$ .

$(m + 2) (2 m^{2} + 3 m - 6 - 2 m + 4)$

Subtract $2 m$ from $3 m$ .

$(m + 2) (2 m^{2} + m - 6 + 4)$

Add $- 6$ and $4$ .

$(m + 2) (2 m^{2} + m - 2)$

Step 2

Expand $(m + 2) (2 m^{2} + m - 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 3

Simplify terms.

Combine the opposite terms in $m (2 m^{2}) + m \cdot m + m \cdot - 2 + 2 (2 m^{2}) + 2 m + 2 \cdot - 2$ .

Reorder the factors in the terms $m \cdot - 2$ and $2 m$ .

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

Add $- 2 m$ and $2 m$ .

$m (2 m^{2}) + m \cdot m + 2 (2 m^{2}) + 0 + 2 \cdot - 2$

Add $m (2 m^{2}) + m \cdot m + 2 (2 m^{2})$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $m^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $m$ by $m$ .

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

Multiply $2$ by $2$ .

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

Multiply $2$ by $- 2$ .

$2 m^{3} + m^{2} + 4 m^{2} - 4$

Add $m^{2}$ and $4 m^{2}$ .

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