Solve a^3-a^6

$$a ^ { 3 } - a ^ { 6 }$$

Factor

$$\left(a-1\right)\left(-a^{2}-a-1\right)a^{3}$$

Solution Steps

Factor out a^{3}.

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

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.

$$a^{3}\left(a-1\right)\left(-a^{2}-a-1\right)$$

Evaluate

$$a^{3}-a^{6}$$