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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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