Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $y^{2}$ .

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

Step 2.1.2

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

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

Step 2.1.3

Add $2$ and $2$ .

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

Step 2.2

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

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Step 2.2.1

Move $y$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $2$ .

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

Step 2.3

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

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Step 2.3.1

Move $y$ .

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

Step 2.3.2

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

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Step 2.3.2.1

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

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

Step 2.3.2.2

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

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

Step 2.3.3

Add $1$ and $2$ .

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

Step 2.4

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

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Step 2.4.1

Move $z$ .

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

Step 2.4.2

Multiply $z$ by $z$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $z$ .

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

Step 3.1.2

Multiply $z$ by $z$ .

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

Step 3.2

Multiply $2$ by $3$ .

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

Step 3.3

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

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Step 3.3.1

Move $z$ .

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

Step 3.3.2

Multiply $z$ by $z$ .

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

Step 3.4

Multiply $4$ by $3$ .

$6 y^{4} z^{2} + 12 y^{3} z^{2} + 3 y^{3} z \cdot - 1 + 3 y^{2} z^{2}$

Step 3.5

Multiply $- 1$ by $3$ .

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