Solve 20a^2b-50a^3-2ab^2

$$20 a ^ { 2 } b - 50 a ^ { 3 } - 2 a b ^ { 2 }$$

Factor

$$-2a\left(5a-b\right)^{2}$$

Solution Steps

Factor out 2.

$$2\left(10a^{2}b-25a^{3}-ab^{2}\right)$$

Consider 10a^{2}b-25a^{3}-ab^{2}. Factor out a.

$$a\left(10ab-25a^{2}-b^{2}\right)$$

Consider 10ab-25a^{2}-b^{2}. Consider 10ab-25a^{2}-b^{2} as a polynomial over variable a.

$$-25a^{2}+10ba-b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -25a^{2} and n divides the constant factor -b^{2}. One such factor is 5a-b. Factor the polynomial by dividing it by this factor.

$$\left(5a-b\right)\left(-5a+b\right)$$

Rewrite the complete factored expression.

$$2a\left(5a-b\right)\left(-5a+b\right)$$

Evaluate

$$-2a\left(5a-b\right)^{2}$$