Solve 5a^3-20ab^2

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

Factor

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

Solution Steps

Factor out 5.

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

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