Pre-Algebra Examples

$9 x^{2} - 7 x + 9 + (- x^{2} + 5 x + 5) - (- x^{2} + 8 x + 10 + (7 x^{2} + 10 x + 8))$

Step 1

Remove parentheses.

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - (- x^{2} + 8 x + 10 + 7 x^{2} + 10 x + 8)$

Step 2

Simplify each term.

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Step 2.1

Add $- x^{2}$ and $7 x^{2}$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - (6 x^{2} + 8 x + 10 + 10 x + 8)$

Step 2.2

Add $8 x$ and $10 x$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - (6 x^{2} + 18 x + 10 + 8)$

Step 2.3

Add $10$ and $8$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - (6 x^{2} + 18 x + 18)$

Step 2.4

Apply the distributive property.

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - (6 x^{2}) - (18 x) - 1 \cdot 18$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $6$ by $- 1$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - 6 x^{2} - (18 x) - 1 \cdot 18$

Step 2.5.2

Multiply $18$ by $- 1$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - 6 x^{2} - 18 x - 1 \cdot 18$

Step 2.5.3

Multiply $- 1$ by $18$ .

$9 x^{2} - 7 x + 9 - x^{2} + 5 x + 5 - 6 x^{2} - 18 x - 18$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $x^{2}$ from $9 x^{2}$ .

$8 x^{2} - 7 x + 9 + 5 x + 5 - 6 x^{2} - 18 x - 18$

Step 3.2

Subtract $6 x^{2}$ from $8 x^{2}$ .

$2 x^{2} - 7 x + 9 + 5 x + 5 - 18 x - 18$

Step 3.3

Add $- 7 x$ and $5 x$ .

$2 x^{2} - 2 x + 9 + 5 - 18 x - 18$

Step 3.4

Subtract $18 x$ from $- 2 x$ .

$2 x^{2} - 20 x + 9 + 5 - 18$

Step 3.5

Simplify by adding and subtracting.

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Step 3.5.1

Add $9$ and $5$ .

$2 x^{2} - 20 x + 14 - 18$

Step 3.5.2

Subtract $18$ from $14$ .

$2 x^{2} - 20 x - 4$