Finding the Maclaurin series for the given function.

Question

I am dealing with a problem that says:Find the Maclaurin series for the function $f(x)=\ln(1+x+x^2)$.

I have tried to write the expression inside the brackets exactly, $1+x+x^2$ as a product of two other expressions and then by means of the properties of the function $\ln$.

I will divide it into two functions corresponding to $\ln$ whose sums then return to an elementary problem, but $1+x+x^2$ has no real roots, I'm open to other ideas and suggestions on how to find the Maclaurin series for the given function above.

Answer 1

$$1+x+x^2=\frac{1-x^3}{1-x}$$

$$\ln(1+x+x^2)=\ln(1-x^3)-\ln({1-x})$$

Can you proceed from here?