Precalculus Examples

$(- 6 x^{4} - 2 x^{2} + 6 x - 3) - (- 12 x^{5} + 2 x^{3} + x^{2} - 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 6 x^{4} - 2 x^{2} + 6 x - 3 - (- 12 x^{5}) - (2 x^{3}) - x^{2} - - 7$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 12$ by $- 1$ .

$- 6 x^{4} - 2 x^{2} + 6 x - 3 + 12 x^{5} - (2 x^{3}) - x^{2} - - 7$

Step 1.2.2

Multiply $2$ by $- 1$ .

$- 6 x^{4} - 2 x^{2} + 6 x - 3 + 12 x^{5} - 2 x^{3} - x^{2} - - 7$

Step 1.2.3

Multiply $- 1$ by $- 7$ .

$- 6 x^{4} - 2 x^{2} + 6 x - 3 + 12 x^{5} - 2 x^{3} - x^{2} + 7$

Step 2

Simplify by adding terms.

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Step 2.1

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

$- 6 x^{4} - 3 x^{2} + 6 x - 3 + 12 x^{5} - 2 x^{3} + 7$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $- 3$ and $7$ .

$- 6 x^{4} - 3 x^{2} + 6 x + 12 x^{5} - 2 x^{3} + 4$

Step 2.2.2

Move $6 x$ .

$- 6 x^{4} - 3 x^{2} + 12 x^{5} - 2 x^{3} + 6 x + 4$

Step 2.2.3

Move $- 3 x^{2}$ .

$- 6 x^{4} + 12 x^{5} - 2 x^{3} - 3 x^{2} + 6 x + 4$

Step 2.2.4

Reorder $- 6 x^{4}$ and $12 x^{5}$ .

$12 x^{5} - 6 x^{4} - 2 x^{3} - 3 x^{2} + 6 x + 4$