Algebra Examples

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

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.

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Step 2.1

Move $y^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

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.

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Step 3.1

Move $z$ .

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $1$ and $2$ .

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

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $z$ .

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

Step 4.1.2

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

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Step 4.1.2.1

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

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

Step 4.1.2.2

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

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

Step 4.1.3

Add $1$ and $2$ .

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

Step 4.2

Multiply $- 5$ by $- 2$ .

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

Step 4.3

Multiply $- 4$ by $- 2$ .

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