Pre-Algebra Examples

$(3 x^{3} - 2 x^{2} + 4 x - 8) - (5 x^{3} + 12 x^{2} - 3 x - 4)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 x^{3} - 2 x^{2} + 4 x - 8 - (5 x^{3}) - (12 x^{2}) - (- 3 x) - - 4$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$3 x^{3} - 2 x^{2} + 4 x - 8 - 5 x^{3} - (12 x^{2}) - (- 3 x) - - 4$

Step 1.2.2

Multiply $12$ by $- 1$ .

$3 x^{3} - 2 x^{2} + 4 x - 8 - 5 x^{3} - 12 x^{2} - (- 3 x) - - 4$

Step 1.2.3

Multiply $- 3$ by $- 1$ .

$3 x^{3} - 2 x^{2} + 4 x - 8 - 5 x^{3} - 12 x^{2} + 3 x - - 4$

Step 1.2.4

Multiply $- 1$ by $- 4$ .

$3 x^{3} - 2 x^{2} + 4 x - 8 - 5 x^{3} - 12 x^{2} + 3 x + 4$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{3}$ from $3 x^{3}$ .

$- 2 x^{3} - 2 x^{2} + 4 x - 8 - 12 x^{2} + 3 x + 4$

Step 2.2

Subtract $12 x^{2}$ from $- 2 x^{2}$ .

$- 2 x^{3} - 14 x^{2} + 4 x - 8 + 3 x + 4$

Step 2.3

Add $4 x$ and $3 x$ .

$- 2 x^{3} - 14 x^{2} + 7 x - 8 + 4$

Step 2.4

Add $- 8$ and $4$ .

$- 2 x^{3} - 14 x^{2} + 7 x - 4$