Simplify -9g(-2g+g^2)+3(g^2+4)

$- 9 g (- 2 g + g^{2}) + 3 (g^{2} + 4)$

Step 1

Simplify each term.

Apply the distributive property.

$- 9 g (- 2 g) - 9 g \cdot g^{2} + 3 (g^{2} + 4)$

Rewrite using the commutative property of multiplication.

$- 9 \cdot - 2 g \cdot g - 9 g \cdot g^{2} + 3 (g^{2} + 4)$

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

Move $g^{2}$ .

$- 9 \cdot - 2 g \cdot g - 9 (g^{2} g) + 3 (g^{2} + 4)$

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

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

$- 9 \cdot - 2 g \cdot g - 9 (g^{2} g^{1}) + 3 (g^{2} + 4)$

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

$- 9 \cdot - 2 g \cdot g - 9 g^{2 + 1} + 3 (g^{2} + 4)$

Add $2$ and $1$ .

$- 9 \cdot - 2 g \cdot g - 9 g^{3} + 3 (g^{2} + 4)$

Simplify each term.

Multiply $g$ by $g$ by adding the exponents.

Move $g$ .

$- 9 \cdot - 2 (g \cdot g) - 9 g^{3} + 3 (g^{2} + 4)$

Multiply $g$ by $g$ .

$- 9 \cdot - 2 g^{2} - 9 g^{3} + 3 (g^{2} + 4)$

Multiply $- 9$ by $- 2$ .

$18 g^{2} - 9 g^{3} + 3 (g^{2} + 4)$

Apply the distributive property.

$18 g^{2} - 9 g^{3} + 3 g^{2} + 3 \cdot 4$

Multiply $3$ by $4$ .

$18 g^{2} - 9 g^{3} + 3 g^{2} + 12$

Step 2

Add $18 g^{2}$ and $3 g^{2}$ .

$- 9 g^{3} + 21 g^{2} + 12$