Algebra Examples

$(- 12 a z^{2} - 2 z^{3}) + (- 2 a^{3} + 7 a^{2} z) - (- 4 a^{2} z + 8 a z^{2})$

Step 1

Remove parentheses.

$- 12 a z^{2} - 2 z^{3} - 2 a^{3} + 7 a^{2} z - (- 4 a^{2} z + 8 a z^{2})$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 12 a z^{2} - 2 z^{3} - 2 a^{3} + 7 a^{2} z - (- 4 a^{2} z) - (8 a z^{2})$

Step 2.2

Multiply $- 4$ by $- 1$ .

$- 12 a z^{2} - 2 z^{3} - 2 a^{3} + 7 a^{2} z + 4 (a^{2} z) - (8 a z^{2})$

Step 2.3

Multiply $8$ by $- 1$ .

$- 12 a z^{2} - 2 z^{3} - 2 a^{3} + 7 a^{2} z + 4 (a^{2} z) - 8 (a z^{2})$

Step 2.4

Remove parentheses.

$- 12 a z^{2} - 2 z^{3} - 2 a^{3} + 7 a^{2} z + 4 a^{2} z - 8 a z^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $8 a z^{2}$ from $- 12 a z^{2}$ .

$- 2 z^{3} - 2 a^{3} + 7 a^{2} z + 4 a^{2} z - 20 a z^{2}$

Step 3.2

Add $7 a^{2} z$ and $4 a^{2} z$ .

$- 2 z^{3} - 2 a^{3} + 11 a^{2} z - 20 a z^{2}$

Step 3.3

Move $- 2 z^{3}$ .

$- 2 a^{3} + 11 a^{2} z - 20 a z^{2} - 2 z^{3}$