Simplify -7y^3(4y^2+y-3)

$- 7 y^{3} (4 y^{2} + y - 3)$

Step 1

Apply the distributive property.

$- 7 y^{3} (4 y^{2}) - 7 y^{3} y - 7 y^{3} \cdot - 3$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 7 \cdot 4 y^{3} y^{2} - 7 y^{3} y - 7 y^{3} \cdot - 3$

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

Move $y$ .

$- 7 \cdot 4 y^{3} y^{2} - 7 (y \cdot y^{3}) - 7 y^{3} \cdot - 3$

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

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

$- 7 \cdot 4 y^{3} y^{2} - 7 (y^{1} y^{3}) - 7 y^{3} \cdot - 3$

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

$- 7 \cdot 4 y^{3} y^{2} - 7 y^{1 + 3} - 7 y^{3} \cdot - 3$

Add $1$ and $3$ .

$- 7 \cdot 4 y^{3} y^{2} - 7 y^{4} - 7 y^{3} \cdot - 3$

Multiply $- 3$ by $- 7$ .

$- 7 \cdot 4 y^{3} y^{2} - 7 y^{4} + 21 y^{3}$

Step 3

Simplify each term.

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

Move $y^{2}$ .

$- 7 \cdot 4 (y^{2} y^{3}) - 7 y^{4} + 21 y^{3}$

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

$- 7 \cdot 4 y^{2 + 3} - 7 y^{4} + 21 y^{3}$

Add $2$ and $3$ .

$- 7 \cdot 4 y^{5} - 7 y^{4} + 21 y^{3}$

Multiply $- 7$ by $4$ .

$- 28 y^{5} - 7 y^{4} + 21 y^{3}$