Calculus Examples

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

Step 1

Combine the opposite terms in $(- 4 x^{2} - 4 x - 7) - (- 3 x^{2} + 8 x - 2) + 2 x^{2} + 7 - 2$ .

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Step 1.1

Add $- 7$ and $7$ .

$- 4 x^{2} - 4 x + 0 - (- 3 x^{2} + 8 x - 2) + 2 x^{2} - 2$

Step 1.2

Add $- 4 x^{2} - 4 x$ and $0$ .

$- 4 x^{2} - 4 x - (- 3 x^{2} + 8 x - 2) + 2 x^{2} - 2$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 4 x^{2} - 4 x - (- 3 x^{2}) - (8 x) - - 2 + 2 x^{2} - 2$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 3$ by $- 1$ .

$- 4 x^{2} - 4 x + 3 x^{2} - (8 x) - - 2 + 2 x^{2} - 2$

Step 2.2.2

Multiply $8$ by $- 1$ .

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

Step 2.2.3

Multiply $- 1$ by $- 2$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- 4 x^{2} - 4 x + 3 x^{2} - 8 x + 2 + 2 x^{2} - 2$ .

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Step 3.1.1

Subtract $2$ from $2$ .

$- 4 x^{2} - 4 x + 3 x^{2} - 8 x + 2 x^{2} + 0$

Step 3.1.2

Add $- 4 x^{2} - 4 x + 3 x^{2} - 8 x + 2 x^{2}$ and $0$ .

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

Step 3.2

Add $- 4 x^{2}$ and $3 x^{2}$ .

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

Step 3.3

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

$x^{2} - 4 x - 8 x$

Step 3.4

Subtract $8 x$ from $- 4 x$ .

$x^{2} - 12 x$