Solve a^0+2a^3+1

$$a ^ { 0 } + 2 a ^ { 3 } + 1$$

Evaluate

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

Solution Steps

Calculate a to the power of 0 and get 1.

$$1+2a^{3}+1$$

Add 1 and 1 to get 2.

$$2+2a^{3}$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$2a^{3}+2$$

Factor out 2.

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

Consider a^{3}+1. Rewrite a^{3}+1 as a^{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).

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

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

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