Simplify 4y(-y^3-2y-1)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $4$ .

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

Step 3

Simplify each term.

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

Move $y^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $4$ by $- 2$ .

$- 4 y^{4} - 8 y^{2} - 4 y$