Solve (x^3-2x-1)-(3x^3-2x^2-x-1)

$$( x ^ { 3 } - 2 x - 1 ) - ( 3 x ^ { 3 } - 2 x ^ { 2 } - x - 1 )$$

Evaluate

$$x\left(-2x^{2}+2x-1\right)$$

Solution Steps

To find the opposite of 3x^{3}-2x^{2}-x-1, find the opposite of each term.

$$x^{3}-2x-1-3x^{3}+2x^{2}+x+1$$

Combine x^{3} and -3x^{3} to get -2x^{3}.

$$-2x^{3}-2x-1+2x^{2}+x+1$$

Combine -2x and x to get -x.

$$-2x^{3}-x-1+2x^{2}+1$$

Add -1 and 1 to get 0.

$$-2x^{3}-x+2x^{2}$$

Expand

$$-2x^{3}+2x^{2}-x$$

Solution Steps

To find the opposite of 3x^{3}-2x^{2}-x-1, find the opposite of each term.

$$x^{3}-2x-1-3x^{3}+2x^{2}+x+1$$

Combine x^{3} and -3x^{3} to get -2x^{3}.

$$-2x^{3}-2x-1+2x^{2}+x+1$$

Combine -2x and x to get -x.

$$-2x^{3}-x-1+2x^{2}+1$$

Add -1 and 1 to get 0.

$$-2x^{3}-x+2x^{2}$$