Simplify (3x^3-7x^2+12)-(3x^3+6x^2+10x)

$(3 x^{3} - 7 x^{2} + 12) - (3 x^{3} + 6 x^{2} + 10 x)$

Step 1

Simplify each term.

Apply the distributive property.

$3 x^{3} - 7 x^{2} + 12 - (3 x^{3}) - (6 x^{2}) - (10 x)$

Simplify.

Multiply $3$ by $- 1$ .

$3 x^{3} - 7 x^{2} + 12 - 3 x^{3} - (6 x^{2}) - (10 x)$

Multiply $6$ by $- 1$ .

$3 x^{3} - 7 x^{2} + 12 - 3 x^{3} - 6 x^{2} - (10 x)$

Multiply $10$ by $- 1$ .

$3 x^{3} - 7 x^{2} + 12 - 3 x^{3} - 6 x^{2} - 10 x$

Step 2

Simplify by adding terms.

Combine the opposite terms in $3 x^{3} - 7 x^{2} + 12 - 3 x^{3} - 6 x^{2} - 10 x$ .

Subtract $3 x^{3}$ from $3 x^{3}$ .

$- 7 x^{2} + 12 + 0 - 6 x^{2} - 10 x$

Add $- 7 x^{2} + 12$ and $0$ .

$- 7 x^{2} + 12 - 6 x^{2} - 10 x$

Subtract $6 x^{2}$ from $- 7 x^{2}$ .

$- 13 x^{2} + 12 - 10 x$

Move $12$ .

$- 13 x^{2} - 10 x + 12$