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.
Best Answer
$(1+2x)^4$ give out terms containing $x$ with power $0,1,2,3,4$ similarly $(2+x)^{10}$ give out term containing $x$ with power $0$ to $10$ now pick up exponents from first and second such that these sum up to 13 along with coefficient. ATP, $$(10{C_0}x^{10})(4C_3(2x)^3)+2(10C_1x^9)(4C_4(2x)^4)$$ and these will give out coefficient.