Pre-Algebra Examples

$(9 w^{2} - 5 w + 2) - (- 7 w^{2} - 5 w + 1) + (2 w^{2} + 2 w + 9)$

Step 1

Remove parentheses.

$(9 w^{2} - 5 w + 2) - (- 7 w^{2} - 5 w + 1) + 2 w^{2} + 2 w + 9$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$9 w^{2} - 5 w + 2 - (- 7 w^{2}) - (- 5 w) - 1 \cdot 1 + 2 w^{2} + 2 w + 9$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 7$ by $- 1$ .

$9 w^{2} - 5 w + 2 + 7 w^{2} - (- 5 w) - 1 \cdot 1 + 2 w^{2} + 2 w + 9$

Step 2.2.2

Multiply $- 5$ by $- 1$ .

$9 w^{2} - 5 w + 2 + 7 w^{2} + 5 w - 1 \cdot 1 + 2 w^{2} + 2 w + 9$

Step 2.2.3

Multiply $- 1$ by $1$ .

$9 w^{2} - 5 w + 2 + 7 w^{2} + 5 w - 1 + 2 w^{2} + 2 w + 9$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $9 w^{2} - 5 w + 2 + 7 w^{2} + 5 w - 1 + 2 w^{2} + 2 w + 9$ .

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Step 3.1.1

Add $- 5 w$ and $5 w$ .

$9 w^{2} + 2 + 7 w^{2} + 0 - 1 + 2 w^{2} + 2 w + 9$

Step 3.1.2

Add $9 w^{2} + 2 + 7 w^{2}$ and $0$ .

$9 w^{2} + 2 + 7 w^{2} - 1 + 2 w^{2} + 2 w + 9$

Step 3.2

Add $9 w^{2}$ and $7 w^{2}$ .

$16 w^{2} + 2 - 1 + 2 w^{2} + 2 w + 9$

Step 3.3

Add $16 w^{2}$ and $2 w^{2}$ .

$18 w^{2} + 2 - 1 + 2 w + 9$

Step 3.4

Simplify by adding and subtracting.

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Step 3.4.1

Subtract $1$ from $2$ .

$18 w^{2} + 1 + 2 w + 9$

Step 3.4.2

Add $1$ and $9$ .

$18 w^{2} + 2 w + 10$