Solve a^3+a^2b-ab-a^2

$$a ^ { 3 } + a ^ { 2 } b - a b - a ^ { 2 }$$

Factor

$$a\left(a-1\right)\left(a+b\right)$$

Solution Steps

Factor out a.

$$a\left(a^{2}+ab-b-a\right)$$

Consider a^{2}+ab-b-a. Do the grouping a^{2}+ab-b-a=\left(a^{2}+ab\right)+\left(-b-a\right), and factor out a in the first and -1 in the second group.

$$a\left(a+b\right)-\left(a+b\right)$$

Factor out common term a+b by using distributive property.

$$\left(a+b\right)\left(a-1\right)$$

Rewrite the complete factored expression.

$$a\left(a+b\right)\left(a-1\right)$$

Evaluate

$$a\left(a-1\right)\left(a+b\right)$$