Find the coefficient of $ x^6 y^8 $in the expansion of:

Question

Find the coefficient of $x^6 y^8$ in the expansion of: $$\left(4x+\frac{y}{2}\right)^{14}$$

Answer 1

Apply $$(a + b)^n =\sum_{k=0}^n {n\choose k} a^k b^{n-k}.$$ For which $k$ do you get an $x^6y^8$ term?

Answer 2

Hint: Write $$\left(4x + \frac{1}{2}y\right)^{14} = \sum_{i=0}^{14} \binom{14}{i} (4x)^i \left(\frac{1}{2}y\right)^{14-i}$$