Find the Product -2yz^2*(-5y^2z-4z)

$- 2 y z^{2} \cdot (- 5 y^{2} z - 4 z)$

Step 1

Apply the distributive property.

$- 2 y z^{2} (- 5 y^{2} z) - 2 y z^{2} (- 4 z)$

Step 2

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

Move $y^{2}$ .

$- 2 (y^{2} y) z^{2} (- 5 z) - 2 y z^{2} (- 4 z)$

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

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

$- 2 (y^{2} y^{1}) z^{2} (- 5 z) - 2 y z^{2} (- 4 z)$

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

$- 2 y^{2 + 1} z^{2} (- 5 z) - 2 y z^{2} (- 4 z)$

Add $2$ and $1$ .

$- 2 y^{3} z^{2} (- 5 z) - 2 y z^{2} (- 4 z)$

Step 3

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

Move $z$ .

$- 2 y^{3} z^{2} (- 5 z) - 2 y (z \cdot z^{2}) \cdot - 4$

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

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

$- 2 y^{3} z^{2} (- 5 z) - 2 y (z^{1} z^{2}) \cdot - 4$

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

$- 2 y^{3} z^{2} (- 5 z) - 2 y z^{1 + 2} \cdot - 4$

Add $1$ and $2$ .

$- 2 y^{3} z^{2} (- 5 z) - 2 y z^{3} \cdot - 4$

Step 4

Simplify each term.

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

Move $z$ .

$- 2 y^{3} (z \cdot z^{2}) \cdot - 5 - 2 y z^{3} \cdot - 4$

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

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

$- 2 y^{3} (z^{1} z^{2}) \cdot - 5 - 2 y z^{3} \cdot - 4$

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

$- 2 y^{3} z^{1 + 2} \cdot - 5 - 2 y z^{3} \cdot - 4$

Add $1$ and $2$ .

$- 2 y^{3} z^{3} \cdot - 5 - 2 y z^{3} \cdot - 4$

Multiply $- 5$ by $- 2$ .

$10 y^{3} z^{3} - 2 y z^{3} \cdot - 4$

Multiply $- 4$ by $- 2$ .

$10 y^{3} z^{3} + 8 y z^{3}$