Algebra Examples

$(x^{3} - 3 x + 1) - (x^{3} + 7 - 12 x)$

Step 1

Regroup terms.

$x^{3} - (x^{3} + 7 - 12 x) - 3 x + 1$

Step 2

Apply the distributive property.

$x^{3} - x^{3} - 1 \cdot 7 - (- 12 x) - 3 x + 1$

Step 3

Simplify.

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Step 3.1

Multiply $- 1$ by $7$ .

$x^{3} - x^{3} - 7 - (- 12 x) - 3 x + 1$

Step 3.2

Multiply $- 12$ by $- 1$ .

$x^{3} - x^{3} - 7 + 12 x - 3 x + 1$

$x^{3} - x^{3} - 7 + 12 x - 3 x + 1$

Step 4

Subtract $x^{3}$ from $x^{3}$ .

$0 - 7 + 12 x - 3 x + 1$

Step 5

Subtract $7$ from $0$ .

$- 7 + 12 x - 3 x + 1$

Step 6

Factor $- 1$ out of $- 7 + 12 x$ .

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Step 6.1

Reorder $- 7$ and $12 x$ .

$12 x - 7 - 3 x + 1$

Step 6.2

Factor $- 1$ out of $12 x$ .

$- (- 12 x) - 7 - 3 x + 1$

Step 6.3

Rewrite $- 7$ as $- 1 (7)$ .

$- (- 12 x) - 1 (7) - 3 x + 1$

Step 6.4

Factor $- 1$ out of $- (- 12 x) - 1 (7)$ .

$- (- 12 x + 7) - 3 x + 1$

$- (- 12 x + 7) - 3 x + 1$

Step 7

Factor $- 1$ out of $- 3 x + 1$ .

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Step 7.1

Factor $- 1$ out of $- 3 x$ .

$- (- 12 x + 7) - (3 x) + 1$

Step 7.2

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

$- (- 12 x + 7) - (3 x) - 1 (- 1)$

Step 7.3

Factor $- 1$ out of $- (3 x) - 1 (- 1)$ .

$- (- 12 x + 7) - (3 x - 1)$

$- (- 12 x + 7) - (3 x - 1)$

Step 8

Factor $- 1$ out of $- (- 12 x + 7) - (3 x - 1)$ .

$- (- 12 x + 7 + 3 x - 1)$

Step 9

Add $- 12 x$ and $3 x$ .

$- (- 9 x + 7 - 1)$

Step 10

Subtract $1$ from $7$ .

$- (- 9 x + 6)$

Step 11

Factor.

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Step 11.1

Factor $3$ out of $- 9 x + 6$ .

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Step 11.1.1

Factor $3$ out of $- 9 x$ .

$- (3 (- 3 x) + 6)$

Step 11.1.2

Factor $3$ out of $6$ .

$- (3 (- 3 x) + 3 (2))$

Step 11.1.3

Factor $3$ out of $3 (- 3 x) + 3 (2)$ .

$- (3 (- 3 x + 2))$

$- (3 (- 3 x + 2))$

Step 11.2

Remove unnecessary parentheses.

$- 1 \cdot 3 (- 3 x + 2)$

$- 1 \cdot 3 (- 3 x + 2)$

Step 12

Multiply $- 1$ by $3$ .

$- 3 (- 3 x + 2)$

Step 13

Factor.

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Step 13.1

Factor $- 1$ out of $- 3 x + 2$ .

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Step 13.1.1

Factor $- 1$ out of $- 3 x$ .

$- 3 (- (3 x) + 2)$

Step 13.1.2

Rewrite $2$ as $- 1 (- 2)$ .

$- 3 (- (3 x) - 1 (- 2))$

Step 13.1.3

Factor $- 1$ out of $- (3 x) - 1 (- 2)$ .

$- 3 (- (3 x - 2))$

$- 3 (- (3 x - 2))$

Step 13.2

Remove unnecessary parentheses.

$- 3 \cdot - 1 (3 x - 2)$

$- 3 \cdot - 1 (3 x - 2)$

Step 14

Combine exponents.

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Step 14.1

Factor out negative.

$- (- 3 (3 x - 2))$

Step 14.2

Multiply $- 3$ by $- 1$ .

$3 (3 x - 2)$

$3 (3 x - 2)$

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