Pre-Algebra Examples

$- z^{3} (9 - z) + 4 z (2 + 3 z)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- z^{3} \cdot 9 - z^{3} (- z) + 4 z (2 + 3 z)$

Step 1.2

Multiply $9$ by $- 1$ .

$- 9 z^{3} - z^{3} (- z) + 4 z (2 + 3 z)$

Step 1.3

Rewrite using the commutative property of multiplication.

$- 9 z^{3} - 1 \cdot - 1 z^{3} z + 4 z (2 + 3 z)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $z$ .

$- 9 z^{3} - 1 \cdot - 1 (z \cdot z^{3}) + 4 z (2 + 3 z)$

Step 1.4.1.2

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

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Step 1.4.1.2.1

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

$- 9 z^{3} - 1 \cdot - 1 (z^{1} z^{3}) + 4 z (2 + 3 z)$

Step 1.4.1.2.2

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

$- 9 z^{3} - 1 \cdot - 1 z^{1 + 3} + 4 z (2 + 3 z)$

Step 1.4.1.3

Add $1$ and $3$ .

$- 9 z^{3} - 1 \cdot - 1 z^{4} + 4 z (2 + 3 z)$

Step 1.4.2

Multiply $- 1$ by $- 1$ .

$- 9 z^{3} + 1 z^{4} + 4 z (2 + 3 z)$

Step 1.4.3

Multiply $z^{4}$ by $1$ .

$- 9 z^{3} + z^{4} + 4 z (2 + 3 z)$

Step 1.5

Apply the distributive property.

$- 9 z^{3} + z^{4} + 4 z \cdot 2 + 4 z (3 z)$

Step 1.6

Multiply $2$ by $4$ .

$- 9 z^{3} + z^{4} + 8 z + 4 z (3 z)$

Step 1.7

Rewrite using the commutative property of multiplication.

$- 9 z^{3} + z^{4} + 8 z + 4 \cdot 3 z \cdot z$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $z$ .

$- 9 z^{3} + z^{4} + 8 z + 4 \cdot 3 (z \cdot z)$

Step 1.8.1.2

Multiply $z$ by $z$ .

$- 9 z^{3} + z^{4} + 8 z + 4 \cdot 3 z^{2}$

Step 1.8.2

Multiply $4$ by $3$ .

$- 9 z^{3} + z^{4} + 8 z + 12 z^{2}$

Step 2

Simplify the expression.

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Step 2.1

Move $8 z$ .

$- 9 z^{3} + z^{4} + 12 z^{2} + 8 z$

Step 2.2

Reorder $- 9 z^{3}$ and $z^{4}$ .

$z^{4} - 9 z^{3} + 12 z^{2} + 8 z$