Solve a^4-a^3b+a^2b-ab^2=

$$a ^ { 4 } - a ^ { 3 } b + a ^ { 2 } b - a b ^ { 2 } =$$

Factor

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

Solution Steps

Factor out a.

$$a\left(a^{3}-a^{2}b+ab-b^{2}\right)$$

Consider a^{3}-a^{2}b+ab-b^{2}. Do the grouping a^{3}-a^{2}b+ab-b^{2}=\left(a^{3}-a^{2}b\right)+\left(ab-b^{2}\right), and factor out a^{2} in the first and b in the second group.

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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