Algebra Examples

$(- 2 x^{2} + x + 1) - (x^{2} - x + 7) - (4 x^{2} + 2 x + 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 x^{2} + x + 1 - x^{2} - - x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - x$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

$- 2 x^{2} + x + 1 - x^{2} + 1 x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Step 1.2.1.2

Multiply $x$ by $1$ .

$- 2 x^{2} + x + 1 - x^{2} + x - 1 \cdot 7 - (4 x^{2} + 2 x + 8)$

Step 1.2.2

Multiply $- 1$ by $7$ .

$- 2 x^{2} + x + 1 - x^{2} + x - 7 - (4 x^{2} + 2 x + 8)$

Step 1.3

Apply the distributive property.

$- 2 x^{2} + x + 1 - x^{2} + x - 7 - (4 x^{2}) - (2 x) - 1 \cdot 8$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $4$ by $- 1$ .

$- 2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - (2 x) - 1 \cdot 8$

Step 1.4.2

Multiply $2$ by $- 1$ .

$- 2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - 2 x - 1 \cdot 8$

Step 1.4.3

Multiply $- 1$ by $8$ .

$- 2 x^{2} + x + 1 - x^{2} + x - 7 - 4 x^{2} - 2 x - 8$

Step 2

Simplify by adding terms.

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Step 2.1

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

$- 3 x^{2} + x + 1 + x - 7 - 4 x^{2} - 2 x - 8$

Step 2.2

Subtract $4 x^{2}$ from $- 3 x^{2}$ .

$- 7 x^{2} + x + 1 + x - 7 - 2 x - 8$

Step 2.3

Add $x$ and $x$ .

$- 7 x^{2} + 2 x + 1 - 7 - 2 x - 8$

Step 2.4

Combine the opposite terms in $- 7 x^{2} + 2 x + 1 - 7 - 2 x - 8$ .

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Step 2.4.1

Subtract $2 x$ from $2 x$ .

$- 7 x^{2} + 0 + 1 - 7 - 8$

Step 2.4.2

Add $- 7 x^{2}$ and $0$ .

$- 7 x^{2} + 1 - 7 - 8$

Step 2.5

Simplify by subtracting numbers.

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Step 2.5.1

Subtract $7$ from $1$ .

$- 7 x^{2} - 6 - 8$

Step 2.5.2

Subtract $8$ from $- 6$ .

$- 7 x^{2} - 14$