Solve 2xleft(x^2+1right)-3xleft(x^2-x+1right)-left(-x^3+x^2-xright)

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

Evaluate

$$2x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

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

Combine -x^{3} and x^{3} to get 0.

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

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

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

Combine -x and x to get 0.

$$2x^{2}$$

Expand

$$2x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

Multiply -1 and -1 to get 1.

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

Combine -x^{3} and x^{3} to get 0.

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

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

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

Combine -x and x to get 0.

$$2x^{2}$$