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

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

Factor

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

Solution Steps

Consider a^{2}-ba-a^{2}b+b^{3} as a polynomial over variable a.

$$\left(1-b\right)a^{2}-ba+b^{3}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power \left(1-b\right)a^{2} and n divides the constant factor b^{3}. One such factor is a-b. Factor the polynomial by dividing it by this factor.

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

Evaluate

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