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

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

Evaluate

$$-x$$

Solution Steps

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

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

Use the distributive property to multiply \left(-x\right)x-x by x-1 and combine like terms.

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

Multiply -1 and -1 to get 1.

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

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

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

Combine x and -2x to get -x.

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

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

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

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

$$-x$$

Expand

$$-x$$

Solution Steps

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

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

Use the distributive property to multiply \left(-x\right)x-x by x-1 and combine like terms.

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

Multiply -1 and -1 to get 1.

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

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

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

Combine x and -2x to get -x.

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

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

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

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

$$-x$$