Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 3$ by $- 1$ .

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

Step 2.2.2

Multiply $7$ by $- 1$ .

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

Step 2.2.3

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 3

Simplify by adding terms.

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Step 3.1

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 3.1.1

Subtract $7 w z$ from $7 w z$ .

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

Step 3.1.2

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 3.2

Add $3 w^{2}$ and $3 w^{2}$ .

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

Step 3.3

Subtract $5 z^{2}$ from $- 5 z^{2}$ .

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