Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 1$ by $7$ .

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

Step 1.2.2

Multiply $- 12$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $x^{3} - 3 x + 1 - x^{3} - 7 + 12 x$ .

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Step 2.1.1

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

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

Step 2.1.2

Add $- 3 x + 1$ and $0$ .

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

Step 2.2

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

$9 x + 1 - 7$

Step 2.3

Subtract $7$ from $1$ .

$9 x - 6$