Find the coefficient of x^6 in the binomial expression of (2x+3) ^9

By the Binomial Theorem:

(a + b) ^n = sum (k=0 to n) [C (n, k) * a^ (n - k) * b^k].

By letting a = 2x, b = 3, and n = 9

(2x + 3) ^9 = sum (k=0 to 9) [C (9, k) * (2x) ^ (9 - k) * 3^k].

As you can see, the power of x is 9 - k. Since we want the x^6 term:

9 - k = 6 = = > k = 3

Thus, letting k = 3 yields the term containing x^6 to be:

C (9, 6) * (2x) ^ (9 - 3) * 3^4 = 435456x^6.

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Its 2 bc its in front of the variable