Question

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

Answer 1

Its 2 bc its in front of the variable

Answer 2

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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