Simplify -3y^3(3y-4xy)

$- 3 y^{3} (3 y - 4 x y)$

Step 1

Apply the distributive property.

$- 3 y^{3} (3 y) - 3 y^{3} (- 4 x y)$

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

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

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

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

$- 3 \cdot 3 y^{3} y - 3 y^{1 + 3} (- 4 x)$

Add $1$ and $3$ .

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

Step 4

Simplify each term.

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

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

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

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

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

$- 3 \cdot 3 y^{1 + 3} - 3 y^{4} (- 4 x)$

Add $1$ and $3$ .

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

Multiply $- 3$ by $3$ .

$- 9 y^{4} - 3 y^{4} (- 4 x)$

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $- 4$ .

$- 9 y^{4} + 12 y^{4} x$