Algebra Examples

$(b^{3} + 5 b c + 10 c^{3}) - (12 b^{3} + 6 b c^{2} + c^{3})$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$b^{3} + 5 b c + 10 c^{3} - (12 b^{3}) - (6 b c^{2}) - c^{3}$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $12$ by $- 1$ .

$b^{3} + 5 b c + 10 c^{3} - 12 b^{3} - (6 b c^{2}) - c^{3}$

Step 2.2.2

Multiply $6$ by $- 1$ .

$b^{3} + 5 b c + 10 c^{3} - 12 b^{3} - 6 (b c^{2}) - c^{3}$

$b^{3} + 5 b c + 10 c^{3} - 12 b^{3} - 6 b c^{2} - c^{3}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $12 b^{3}$ from $b^{3}$ .

$- 11 b^{3} + 5 b c + 10 c^{3} - 6 b c^{2} - c^{3}$

Step 3.2

Subtract $c^{3}$ from $10 c^{3}$ .

$- 11 b^{3} + 5 b c + 9 c^{3} - 6 b c^{2}$

Step 3.3

Reorder.

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Step 3.3.1

Move $5 b c$ .

$- 11 b^{3} + 9 c^{3} - 6 b c^{2} + 5 b c$

Step 3.3.2

Move $9 c^{3}$ .

$- 11 b^{3} - 6 b c^{2} + 9 c^{3} + 5 b c$