Pre-Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.1

Move $x$ .

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

Step 2.1.2

Multiply $x$ by $x$ .

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

Step 2.2

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

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Step 2.2.1

Move $x^{2}$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $2$ and $1$ .

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

Step 2.3

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

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Step 2.3.1

Move $y$ .

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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

Step 2.3.3

Add $1$ and $2$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $y$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

Add $1$ and $2$ .

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

Step 3.2

Multiply $2$ by $- 3$ .

$- 6 x^{2} y^{3} z - 3 x^{3} y^{2} z (5 z) - 3 x y^{3} z (- 4 z^{3})$

Step 3.3

Multiply $z$ by $z$ by adding the exponents.

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Step 3.3.1

Move $z$ .

$- 6 x^{2} y^{3} z - 3 x^{3} y^{2} (z \cdot z) \cdot 5 - 3 x y^{3} z (- 4 z^{3})$

Step 3.3.2

Multiply $z$ by $z$ .

$- 6 x^{2} y^{3} z - 3 x^{3} y^{2} z^{2} \cdot 5 - 3 x y^{3} z (- 4 z^{3})$

Step 3.4

Multiply $5$ by $- 3$ .

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} - 3 x y^{3} z (- 4 z^{3})$

Step 3.5

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

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Step 3.5.1

Move $z^{3}$ .

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} - 3 x y^{3} (z^{3} z) \cdot - 4$

Step 3.5.2

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

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Step 3.5.2.1

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

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} - 3 x y^{3} (z^{3} z^{1}) \cdot - 4$

Step 3.5.2.2

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

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} - 3 x y^{3} z^{3 + 1} \cdot - 4$

Step 3.5.3

Add $3$ and $1$ .

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} - 3 x y^{3} z^{4} \cdot - 4$

Step 3.6

Multiply $- 4$ by $- 3$ .

$- 6 x^{2} y^{3} z - 15 x^{3} y^{2} z^{2} + 12 x y^{3} z^{4}$