Solve (1+x)*(x-1)*x-(x^2-2x+1)*x-2x^2

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

Evaluate

$$-2x$$

Solution Steps

Use the distributive property to multiply 1+x by x-1 and combine like terms.

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

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

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

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

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

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

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

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

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

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

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

Combine 2x^{2} and -2x^{2} to get 0.

$$-2x$$

Expand

$$-2x$$

Solution Steps

Use the distributive property to multiply 1+x by x-1 and combine like terms.

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

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

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

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

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

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

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

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

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

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

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

Combine 2x^{2} and -2x^{2} to get 0.

$$-2x$$