Algebra Examples

$(x^{2} + 6 x + 6 x^{3}) - (3 x - 8 x^{2} - 4 x^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x^{2} + 6 x + 6 x^{3} - (3 x) - (- 8 x^{2}) - (- 4 x^{3})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $- 1$ .

$x^{2} + 6 x + 6 x^{3} - 3 x - (- 8 x^{2}) - (- 4 x^{3})$

Step 1.2.2

Multiply $- 8$ by $- 1$ .

$x^{2} + 6 x + 6 x^{3} - 3 x + 8 x^{2} - (- 4 x^{3})$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$x^{2} + 6 x + 6 x^{3} - 3 x + 8 x^{2} + 4 x^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $x^{2}$ and $8 x^{2}$ .

$9 x^{2} + 6 x + 6 x^{3} - 3 x + 4 x^{3}$

Step 2.2

Subtract $3 x$ from $6 x$ .

$9 x^{2} + 6 x^{3} + 3 x + 4 x^{3}$

Step 2.3

Add $6 x^{3}$ and $4 x^{3}$ .

$9 x^{2} + 10 x^{3} + 3 x$

Step 2.4

Reorder $9 x^{2}$ and $10 x^{3}$ .

$10 x^{3} + 9 x^{2} + 3 x$