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

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

Evaluate

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

Solution Steps

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

$$x^{2}+1-3x\left(x^{2}-x+1\right)-\left(-x^{3}\right)-x^{2}+x$$

Use the distributive property to multiply -3x by x^{2}-x+1.

$$x^{2}+1-3x^{3}+3x^{2}-3x-\left(-x^{3}\right)-x^{2}+x$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$4x^{2}+1-3x^{3}-3x-\left(-x^{3}\right)-x^{2}+x$$

Multiply -1 and -1 to get 1.

$$4x^{2}+1-3x^{3}-3x+x^{3}-x^{2}+x$$

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

$$4x^{2}+1-2x^{3}-3x-x^{2}+x$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

Combine -3x and x to get -2x.

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

Expand

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

Solution Steps

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

$$x^{2}+1-3x\left(x^{2}-x+1\right)-\left(-x^{3}\right)-x^{2}+x$$

Use the distributive property to multiply -3x by x^{2}-x+1.

$$x^{2}+1-3x^{3}+3x^{2}-3x-\left(-x^{3}\right)-x^{2}+x$$

Combine x^{2} and 3x^{2} to get 4x^{2}.

$$4x^{2}+1-3x^{3}-3x-\left(-x^{3}\right)-x^{2}+x$$

Multiply -1 and -1 to get 1.

$$4x^{2}+1-3x^{3}-3x+x^{3}-x^{2}+x$$

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

$$4x^{2}+1-2x^{3}-3x-x^{2}+x$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

Combine -3x and x to get -2x.

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