Algebra Examples

$(2 x^{2} - 13 x + 7) - (1 - 12 x)$

Step 1

Regroup terms.

$- 13 x + 2 x^{2} + 7 - (1 - 12 x)$

Step 2

Apply the distributive property.

$- 13 x + 2 x^{2} + 7 - 1 \cdot 1 - (- 12 x)$

Step 3

Multiply $- 1$ by $1$ .

$- 13 x + 2 x^{2} + 7 - 1 - (- 12 x)$

Step 4

Multiply $- 12$ by $- 1$ .

$- 13 x + 2 x^{2} + 7 - 1 + 12 x$

Step 5

Subtract $1$ from $7$ .

$- 13 x + 2 x^{2} + 6 + 12 x$

Step 6

Reorder terms.

$- 13 x + 2 x^{2} + 12 x + 6$

Step 7

Factor $2$ out of $2 x^{2} + 12 x + 6$ .

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Step 7.1

Factor $2$ out of $2 x^{2}$ .

$- 13 x + 2 (x^{2}) + 12 x + 6$

Step 7.2

Factor $2$ out of $12 x$ .

$- 13 x + 2 (x^{2}) + 2 (6 x) + 6$

Step 7.3

Factor $2$ out of $6$ .

$- 13 x + 2 x^{2} + 2 (6 x) + 2 \cdot 3$

Step 7.4

Factor $2$ out of $2 x^{2} + 2 (6 x)$ .

$- 13 x + 2 (x^{2} + 6 x) + 2 \cdot 3$

Step 7.5

Factor $2$ out of $2 (x^{2} + 6 x) + 2 \cdot 3$ .

$- 13 x + 2 (x^{2} + 6 x + 3)$

$- 13 x + 2 (x^{2} + 6 x + 3)$

Step 8

Factor $- 1$ out of $- 13 x + 2 (x^{2} + 6 x + 3)$ .

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Step 8.1

Reorder $- 13 x$ and $2 (x^{2} + 6 x + 3)$ .

$2 (x^{2} + 6 x + 3) - 13 x$

Step 8.2

Factor $- 1$ out of $2 (x^{2} + 6 x + 3)$ .

$- (- 2 (x^{2} + 6 x + 3)) - 13 x$

Step 8.3

Factor $- 1$ out of $- 13 x$ .

$- (- 2 (x^{2} + 6 x + 3)) - (13 x)$

Step 8.4

Factor $- 1$ out of $- (- 2 (x^{2} + 6 x + 3)) - (13 x)$ .

$- (- 2 (x^{2} + 6 x + 3) + 13 x)$

$- (- 2 (x^{2} + 6 x + 3) + 13 x)$

Step 9

Apply the distributive property.

$- (- 2 x^{2} - 2 (6 x) - 2 \cdot 3 + 13 x)$

Step 10

Simplify.

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Step 10.1

Multiply $6$ by $- 2$ .

$- (- 2 x^{2} - 12 x - 2 \cdot 3 + 13 x)$

Step 10.2

Multiply $- 2$ by $3$ .

$- (- 2 x^{2} - 12 x - 6 + 13 x)$

$- (- 2 x^{2} - 12 x - 6 + 13 x)$

Step 11

Add $- 12 x$ and $13 x$ .

$- (- 2 x^{2} + x - 6)$

Step 12

Factor.

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Step 12.1

Factor $- 1$ out of $- 2 x^{2} + x - 6$ .

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Step 12.1.1

Factor $- 1$ out of $- 2 x^{2}$ .

$- (- (2 x^{2}) + x - 6)$

Step 12.1.2

Factor $- 1$ out of $x$ .

$- (- (2 x^{2}) - 1 (- x) - 6)$

Step 12.1.3

Rewrite $- 6$ as $- 1 (6)$ .

$- (- (2 x^{2}) - 1 (- x) - 1 (6))$

Step 12.1.4

Factor $- 1$ out of $- (2 x^{2}) - 1 (- x)$ .

$- (- (2 x^{2} - x) - 1 (6))$

Step 12.1.5

Factor $- 1$ out of $- (2 x^{2} - x) - 1 (6)$ .

$- - (2 x^{2} - x + 6)$

$- - (2 x^{2} - x + 6)$

Step 12.2

Remove unnecessary parentheses.

$- - 1 (2 x^{2} - x + 6)$

$- - 1 (2 x^{2} - x + 6)$

Step 13

Combine exponents.

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Step 13.1

Factor out negative.

$- - (2 x^{2} - x + 6)$

Step 13.2

Multiply $- 1$ by $- 1$ .

$1 (2 x^{2} - x + 6)$

Step 13.3

Multiply $2 x^{2} - x + 6$ by $1$ .

$2 x^{2} - x + 6$

$2 x^{2} - x + 6$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$