Basic Math Examples

$- z^{2} (3 - z - 2 z^{2})$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Multiply $3$ by $- 1$ .

$- 3 z^{2} - z^{2} (- z) - z^{2} (- 2 z^{2})$

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Rewrite using the commutative property of multiplication.

$- 3 z^{2} - 1 \cdot - 1 z^{2} z - 1 \cdot - 2 z^{2} z^{2}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $z$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

Add $1$ and $2$ .

$- 3 z^{2} - 1 \cdot - 1 z^{3} - 1 \cdot - 2 z^{2} z^{2}$

Step 3.2

Multiply $- 1$ by $- 1$ .

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

Step 3.3

Multiply $z^{3}$ by $1$ .

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

Step 3.4

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

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Step 3.4.1

Move $z^{2}$ .

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

Step 3.4.2

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

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

Step 3.4.3

Add $2$ and $2$ .

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

Step 3.5

Multiply $- 1$ by $- 2$ .

$- 3 z^{2} + z^{3} + 2 z^{4}$