Simplify -8y^3(7y^2-4y-1)

$- 8 y^{3} (7 y^{2} - 4 y - 1)$

Step 1

Apply the distributive property.

$- 8 y^{3} (7 y^{2}) - 8 y^{3} (- 4 y) - 8 y^{3} \cdot - 1$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 8 \cdot 7 y^{3} y^{2} - 8 y^{3} (- 4 y) - 8 y^{3} \cdot - 1$

Rewrite using the commutative property of multiplication.

$- 8 \cdot 7 y^{3} y^{2} - 8 \cdot - 4 y^{3} y - 8 y^{3} \cdot - 1$

Multiply $- 1$ by $- 8$ .

$- 8 \cdot 7 y^{3} y^{2} - 8 \cdot - 4 y^{3} y + 8 y^{3}$

Step 3

Simplify each term.

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

Move $y^{2}$ .

$- 8 \cdot 7 (y^{2} y^{3}) - 8 \cdot - 4 y^{3} y + 8 y^{3}$

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

$- 8 \cdot 7 y^{2 + 3} - 8 \cdot - 4 y^{3} y + 8 y^{3}$

Add $2$ and $3$ .

$- 8 \cdot 7 y^{5} - 8 \cdot - 4 y^{3} y + 8 y^{3}$

Multiply $- 8$ by $7$ .

$- 56 y^{5} - 8 \cdot - 4 y^{3} y + 8 y^{3}$

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

Move $y$ .

$- 56 y^{5} - 8 \cdot - 4 (y \cdot y^{3}) + 8 y^{3}$

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

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

$- 56 y^{5} - 8 \cdot - 4 (y^{1} y^{3}) + 8 y^{3}$

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

$- 56 y^{5} - 8 \cdot - 4 y^{1 + 3} + 8 y^{3}$

Add $1$ and $3$ .

$- 56 y^{5} - 8 \cdot - 4 y^{4} + 8 y^{3}$

Multiply $- 8$ by $- 4$ .

$- 56 y^{5} + 32 y^{4} + 8 y^{3}$