Simplify -y^3(5y+1)+4y^4

$- y^{3} (5 y + 1) + 4 y^{4}$

Step 1

Simplify each term.

Apply the distributive property.

$- y^{3} (5 y) - y^{3} \cdot 1 + 4 y^{4}$

Rewrite using the commutative property of multiplication.

$- 1 \cdot 5 y^{3} y - y^{3} \cdot 1 + 4 y^{4}$

Multiply $- 1$ by $1$ .

$- 1 \cdot 5 y^{3} y - y^{3} + 4 y^{4}$

Simplify each term.

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

Move $y$ .

$- 1 \cdot 5 (y \cdot y^{3}) - y^{3} + 4 y^{4}$

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

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

$- 1 \cdot 5 (y^{1} y^{3}) - y^{3} + 4 y^{4}$

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

$- 1 \cdot 5 y^{1 + 3} - y^{3} + 4 y^{4}$

Add $1$ and $3$ .

$- 1 \cdot 5 y^{4} - y^{3} + 4 y^{4}$

Multiply $- 1$ by $5$ .

$- 5 y^{4} - y^{3} + 4 y^{4}$

Step 2

Add $- 5 y^{4}$ and $4 y^{4}$ .

$- y^{4} - y^{3}$