Algebra Examples

$(3 w^{2} + 7 w z - 5 z^{2}) - (- 3 w^{2} + 7 w z + 5 z^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 w^{2} + 7 w z - 5 z^{2} - (- 3 w^{2}) - (7 w z) - (5 z^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply

$- 3$ by

$- 1$ .

$3 w^{2} + 7 w z - 5 z^{2} + 3 w^{2} - (7 w z) - (5 z^{2})$

Step 1.2.2

Multiply

$7$ by

$- 1$ .

$3 w^{2} + 7 w z - 5 z^{2} + 3 w^{2} - 7 (w z) - (5 z^{2})$

Step 1.2.3

Multiply

$5$ by

$- 1$ .

$3 w^{2} + 7 w z - 5 z^{2} + 3 w^{2} - 7 (w z) - 5 z^{2}$

$3 w^{2} + 7 w z - 5 z^{2} + 3 w^{2} - 7 w z - 5 z^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in

$3 w^{2} + 7 w z - 5 z^{2} + 3 w^{2} - 7 w z - 5 z^{2}$ .

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Step 2.1.1

Subtract

$7 w z$ from

$7 w z$ .

$3 w^{2} - 5 z^{2} + 3 w^{2} + 0 - 5 z^{2}$

Step 2.1.2

Add

$3 w^{2} - 5 z^{2} + 3 w^{2}$ and

$0$ .

$3 w^{2} - 5 z^{2} + 3 w^{2} - 5 z^{2}$

Step 2.2

Add

$3 w^{2}$ and

$3 w^{2}$ .

$6 w^{2} - 5 z^{2} - 5 z^{2}$

Step 2.3

Subtract

$5 z^{2}$ from

$- 5 z^{2}$ .

$6 w^{2} - 10 z^{2}$