How can I find the coefficient of x when the power is greater than the powers of 2 brackets using binomial expansion? I have been given this question:
Find the coefficient of $x^{13}$ in the expansion of $(1 + 2x)^4(2 + x)^{10}$.
I know how I would find $x^4$ or lower degrees, but I am unsure how to approach this, as neither term has a $x^{13}$, and x is a prime number so it can't just be 2 terms multiplied (as neither bracket has a power of 13).
Where do I start with this?
 This is revision rather than homework, but hints would be appreciated.

Since $x^{10}\cdot x^3=x^{13}$ and $x^{9}\cdot x^4=x^{13}$, we just have to find the coefficients of $x^4,x^3$ in $(1+2x)^4$ and the coefficients of $x^{10},x^9$ in $(2+x)^{10}$. To do this you can use binomial thereom:
$$x^3:{4 \choose 3}(2x)^3=32x^3$$
$$x^4:{4 \choose 0}(2x)^4=16x^4$$
$$x^{10}:{10 \choose 0}(x)^{10}=x^{10}$$
$$x^9:{10 \choose 1}2(x)^9=20x^9.$$
So we have $20x^9\cdot 16x^4+32x^3\cdot x^{10}=352x^{13}. $
