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

$$x ( x + 1 ) ( - x + 2 )$$

Evaluate

$$x\left(2-x\right)\left(x+1\right)$$

Solution Steps

Use the distributive property to multiply x by x+1.

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

Apply the distributive property by multiplying each term of x^{2}+x by each term of -x+2.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply x and x to get x^{2}.

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

Combine 2x^{2} and x^{2}\left(-1\right) to get x^{2}.

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

Expand

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

Solution Steps

Use the distributive property to multiply x by x+1.

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

Apply the distributive property by multiplying each term of x^{2}+x by each term of -x+2.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply x and x to get x^{2}.

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

Combine 2x^{2} and x^{2}\left(-1\right) to get x^{2}.

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