Solve 3a+3at^3=

$$3 a + 3 a t ^ { 3 } =$$

Factor

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

Solution Steps

Factor out 3.

$$3\left(a+at^{3}\right)$$

Consider a+at^{3}. Factor out a.

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

Consider 1+t^{3}. Rewrite 1+t^{3} as t^{3}+1^{3}. The sum of cubes can be factored using the rule: p^{3}+q^{3}=\left(p+q\right)\left(p^{2}-pq+q^{2}\right).

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

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

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

Evaluate

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