Find the Product -3y^2(-4y^3+y-9)

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 4 y^{2} y^{3} - 3 y^{2} y - 3 y^{2} \cdot - 9$

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

Move $y$ .

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

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

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

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

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

$- 3 \cdot - 4 y^{2} y^{3} - 3 y^{1 + 2} - 3 y^{2} \cdot - 9$

Add $1$ and $2$ .

$- 3 \cdot - 4 y^{2} y^{3} - 3 y^{3} - 3 y^{2} \cdot - 9$

Multiply $- 9$ by $- 3$ .

$- 3 \cdot - 4 y^{2} y^{3} - 3 y^{3} + 27 y^{2}$

Simplify each term.

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$- 3 \cdot - 4 (y^{3} y^{2}) - 3 y^{3} + 27 y^{2}$

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

$- 3 \cdot - 4 y^{3 + 2} - 3 y^{3} + 27 y^{2}$

Add $3$ and $2$ .

$- 3 \cdot - 4 y^{5} - 3 y^{3} + 27 y^{2}$

Multiply $- 3$ by $- 4$ .

$12 y^{5} - 3 y^{3} + 27 y^{2}$