Simplify -3z^2(z+2)-4(z^2+1)

$- 3 z^{2} (z + 2) - 4 (z^{2} + 1)$

Step 1

Simplify each term.

Apply the distributive property.

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

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

Move $z$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $- 3$ .

$- 3 z^{3} - 6 z^{2} - 4 (z^{2} + 1)$

Apply the distributive property.

$- 3 z^{3} - 6 z^{2} - 4 z^{2} - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$- 3 z^{3} - 6 z^{2} - 4 z^{2} - 4$

Step 2

Subtract $4 z^{2}$ from $- 6 z^{2}$ .

$- 3 z^{3} - 10 z^{2} - 4$