# Greatest term!

Algebra Level 3

Consider the binomial expansion $$(2+3x)^9$$. Let $$\mathbb{P}$$ denote the largest coefficient of all terms when it's expanded.

If $$\left ( \dfrac {3}{2} \right )^6 \times \mathbb{P} = \dfrac {3^a \times b}{c}$$

for natural numbers $$a,b,c$$ with $$\text{gcd}(c,3)=\text{gcd}(b,c) = 1$$.

What is the value of $$a+b+c$$?

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