Precalculus Examples

$2 (3 x^{6} - 9 x^{2} + 2 x) - (5 x^{6} - 10 x^{2} - 4 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 (3 x^{6}) + 2 (- 9 x^{2}) + 2 (2 x) - (5 x^{6} - 10 x^{2} - 4 x)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $2$ .

$6 x^{6} + 2 (- 9 x^{2}) + 2 (2 x) - (5 x^{6} - 10 x^{2} - 4 x)$

Step 1.2.2

Multiply $- 9$ by $2$ .

$6 x^{6} - 18 x^{2} + 2 (2 x) - (5 x^{6} - 10 x^{2} - 4 x)$

Step 1.2.3

Multiply $2$ by $2$ .

$6 x^{6} - 18 x^{2} + 4 x - (5 x^{6} - 10 x^{2} - 4 x)$

Step 1.3

Apply the distributive property.

$6 x^{6} - 18 x^{2} + 4 x - (5 x^{6}) - (- 10 x^{2}) - (- 4 x)$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $5$ by $- 1$ .

$6 x^{6} - 18 x^{2} + 4 x - 5 x^{6} - (- 10 x^{2}) - (- 4 x)$

Step 1.4.2

Multiply $- 10$ by $- 1$ .

$6 x^{6} - 18 x^{2} + 4 x - 5 x^{6} + 10 x^{2} - (- 4 x)$

Step 1.4.3

Multiply $- 4$ by $- 1$ .

$6 x^{6} - 18 x^{2} + 4 x - 5 x^{6} + 10 x^{2} + 4 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{6}$ from $6 x^{6}$ .

$x^{6} - 18 x^{2} + 4 x + 10 x^{2} + 4 x$

Step 2.2

Add $- 18 x^{2}$ and $10 x^{2}$ .

$x^{6} - 8 x^{2} + 4 x + 4 x$

Step 2.3

Add $4 x$ and $4 x$ .

$x^{6} - 8 x^{2} + 8 x$