Solve 4b-4a^3b

$$4 b - 4 a ^ { 3 } b$$

Factor

$$4b\left(a-1\right)\left(-a^{2}-a-1\right)$$

Solution Steps

Factor out 4.

$$4\left(b-a^{3}b\right)$$

Consider b-a^{3}b. Factor out b.

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

Consider 1-a^{3}. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term 1 and q divides the leading coefficient -1. One such root is 1. Factor the polynomial by dividing it by a-1.

$$\left(a-1\right)\left(-a^{2}-a-1\right)$$

Rewrite the complete factored expression. Polynomial -a^{2}-a-1 is not factored since it does not have any rational roots.

$$4b\left(a-1\right)\left(-a^{2}-a-1\right)$$

Evaluate

$$4b-4ba^{3}$$