Basic Math Examples

$- (3 z^{2} + 2 z - (2 z^{2} - 6 z)) + ((6 z^{2} - (5 z - z^{2})) + 2 z^{2})$

Step 1

Remove parentheses.

$- (3 z^{2} + 2 z - (2 z^{2} - 6 z)) + (6 z^{2} - (5 z - z^{2})) + 2 z^{2}$

Step 2

Simplify each term.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- (3 z^{2} + 2 z - (2 z^{2}) - (- 6 z)) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.1.2

Multiply $2$ by $- 1$ .

$- (3 z^{2} + 2 z - 2 z^{2} - (- 6 z)) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.1.3

Multiply $- 6$ by $- 1$ .

$- (3 z^{2} + 2 z - 2 z^{2} + 6 z) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.2

Subtract $2 z^{2}$ from $3 z^{2}$ .

$- (z^{2} + 2 z + 6 z) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.3

Add $2 z$ and $6 z$ .

$- (z^{2} + 8 z) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.4

Apply the distributive property.

$- z^{2} - (8 z) + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.5

Multiply $8$ by $- 1$ .

$- z^{2} - 8 z + 6 z^{2} - (5 z - z^{2}) + 2 z^{2}$

Step 2.6

Apply the distributive property.

$- z^{2} - 8 z + 6 z^{2} - (5 z) - - z^{2} + 2 z^{2}$

Step 2.7

Multiply $5$ by $- 1$ .

$- z^{2} - 8 z + 6 z^{2} - 5 z - - z^{2} + 2 z^{2}$

Step 2.8

Multiply $- - z^{2}$ .

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Step 2.8.1

Multiply $- 1$ by $- 1$ .

$- z^{2} - 8 z + 6 z^{2} - 5 z + 1 z^{2} + 2 z^{2}$

Step 2.8.2

Multiply $z^{2}$ by $1$ .

$- z^{2} - 8 z + 6 z^{2} - 5 z + z^{2} + 2 z^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- z^{2} - 8 z + 6 z^{2} - 5 z + z^{2} + 2 z^{2}$ .

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Step 3.1.1

Add $- z^{2}$ and $z^{2}$ .

$- 8 z + 6 z^{2} - 5 z + 0 + 2 z^{2}$

Step 3.1.2

Add $- 8 z + 6 z^{2} - 5 z$ and $0$ .

$- 8 z + 6 z^{2} - 5 z + 2 z^{2}$

Step 3.2

Subtract $5 z$ from $- 8 z$ .

$6 z^{2} - 13 z + 2 z^{2}$

Step 3.3

Add $6 z^{2}$ and $2 z^{2}$ .

$8 z^{2} - 13 z$