Find the Product -8y^2(2y^2+7y-5)

$- 8 y^{2} (2 y^{2} + 7 y - 5)$

Step 1

Apply the distributive property.

$- 8 y^{2} (2 y^{2}) - 8 y^{2} (7 y) - 8 y^{2} \cdot - 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 8 \cdot 2 y^{2} y^{2} - 8 y^{2} (7 y) - 8 y^{2} \cdot - 5$

Rewrite using the commutative property of multiplication.

$- 8 \cdot 2 y^{2} y^{2} - 8 \cdot 7 y^{2} y - 8 y^{2} \cdot - 5$

Multiply $- 5$ by $- 8$ .

$- 8 \cdot 2 y^{2} y^{2} - 8 \cdot 7 y^{2} y + 40 y^{2}$

Step 3

Simplify each term.

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

Move $y^{2}$ .

$- 8 \cdot 2 (y^{2} y^{2}) - 8 \cdot 7 y^{2} y + 40 y^{2}$

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

$- 8 \cdot 2 y^{2 + 2} - 8 \cdot 7 y^{2} y + 40 y^{2}$

Add $2$ and $2$ .

$- 8 \cdot 2 y^{4} - 8 \cdot 7 y^{2} y + 40 y^{2}$

Multiply $- 8$ by $2$ .

$- 16 y^{4} - 8 \cdot 7 y^{2} y + 40 y^{2}$

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

Move $y$ .

$- 16 y^{4} - 8 \cdot 7 (y \cdot y^{2}) + 40 y^{2}$

Multiply $y$ by $y^{2}$ .

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

$- 16 y^{4} - 8 \cdot 7 (y^{1} y^{2}) + 40 y^{2}$

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

$- 16 y^{4} - 8 \cdot 7 y^{1 + 2} + 40 y^{2}$

Add $1$ and $2$ .

$- 16 y^{4} - 8 \cdot 7 y^{3} + 40 y^{2}$

Multiply $- 8$ by $7$ .

$- 16 y^{4} - 56 y^{3} + 40 y^{2}$