Solve 3a^3b-3a^2b^2-36ab^3

$$3 a ^ { 3 } b - 3 a ^ { 2 } b ^ { 2 } - 36 a b ^ { 3 }$$

Factor

$$3ab\left(a-4b\right)\left(a+3b\right)$$

Solution Steps

Factor out 3.

$$3\left(a^{3}b-a^{2}b^{2}-12ab^{3}\right)$$

Consider a^{3}b-a^{2}b^{2}-12ab^{3}. Factor out ab.

$$ab\left(a^{2}-ab-12b^{2}\right)$$

Consider a^{2}-ab-12b^{2}. Consider a^{2}-ab-12b^{2} as a polynomial over variable a.

$$a^{2}-ba-12b^{2}$$

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{2} and m divides the constant factor -12b^{2}. One such factor is a-4b. Factor the polynomial by dividing it by this factor.

$$\left(a-4b\right)\left(a+3b\right)$$

Rewrite the complete factored expression.

$$3ab\left(a-4b\right)\left(a+3b\right)$$

Evaluate

$$3ab\left(a-4b\right)\left(a+3b\right)$$