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

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

Evaluate

$$-x\left(x-3\right)$$

Solution Steps

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

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

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

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

To find the opposite of x^{3}-2x-1, find the opposite of each term.

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

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

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

Combine x and 2x to get 3x.

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

Add -1 and 1 to get 0.

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

Expand

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

Solution Steps

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

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

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

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

To find the opposite of x^{3}-2x-1, find the opposite of each term.

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

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

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

Combine x and 2x to get 3x.

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

Add -1 and 1 to get 0.

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