Binomial Theorem For Quadratic Equation

[Air]

Question:
Find the coefficient of $x^5$ in $(1+x+x^2)^4$.


Problem:
I have not come across expanding brackets which have $x^2$. I know how to apply the binomial theorem for $(a+b)^n$ or $(1+a)^n$ but have not come across $(1 + ax + ax^2)^n$. They are not explained in my textbooks so I was wondering if you could provide hints or redirect me to a useful link. Thanks.

 

[rock.freak667]

Just use $b=x+x^2$ and if you need to expand out $b^2,b^3,b^4$ just use the terms that will give you $x^5$