Solve (x^2-x)+(x^3-x^2)=

$$( x ^ { 2 } - x ) + ( x ^ { 3 } - x ^ { 2 } ) =$$

Factor

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

Solution Steps

Factor out x.

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

Consider x-1+x^{2}-x. Multiply and combine like terms.

$$x^{2}-1$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Rewrite the complete factored expression.

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

Evaluate

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

Solution Steps

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

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