Solve 20ab^2-5a^3

$$20 a b ^ { 2 } - 5 a ^ { 3 }$$

Factor

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

Solution Steps

Factor out 5.

$$5\left(4ab^{2}-a^{3}\right)$$

Consider 4ab^{2}-a^{3}. Factor out a.

$$a\left(4b^{2}-a^{2}\right)$$

Consider 4b^{2}-a^{2}. Rewrite 4b^{2}-a^{2} as \left(2b\right)^{2}-a^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).

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

Reorder the terms.

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

Rewrite the complete factored expression.

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

Evaluate

$$20ab^{2}-5a^{3}$$