Write in Standard Form (b^3+5bc+10c^3)-(12b^3+6bc^2+c^3)

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

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.

Apply the distributive property.

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

Simplify.

Multiply $12$ by $- 1$ .

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

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.

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

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

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

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

Reorder.

Move $5 b c$ .

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

Move $9 c^{3}$ .

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