Expert: Paul Klarreich - 12/10/2010

Question
QUESTION: The sum is as follows: One of the terms in the expansion of (x+3)^7 is k(x)^5.Determine the value of k.
         Thanks!

ANSWER: Questioner:   Andrea
Country:  Canada
Category:  Advanced Math
Private:  No
 
Subject:  Combinatorics
Question:  The sum is as follows: One of the terms in the expansion of (x+3)^7 is k(x)^5.Determine the value of k.
         Thanks!
........................................
Step 1:  Look up the standard  binomial expansion for (a + b)^n

Step 2: Find the term that has  a^5.  It will have b^(n-5) and  coefficient  C(n,5)

Step 3:  Now match up:

n = 7
a = x
b = 3

Substitute them in, and your term is:

C(7,5) x^5 3^2

The stuff that is:

C(7,5) 3^2

is your 'k'.  You can handle the rest.



---------- FOLLOW-UP ----------

QUESTION: You are the only expert I have seen who doesnt except ratings! But it becomes my duty to tell you thankyou as you have explained me the sum!
         Thanks Very Much!=} =} =}

Answer
QUESTION: You are the only expert I have seen who doesnt except ratings! But it becomes my duty to tell you thankyou as you have explained me the sum!
         Thanks Very Much!=} =} =}
.......................
You're very welcome.
But the word is ACCEPT, not except.  It becomes MY duty to help you with spelling, too.
And the result is a PRODUCT, not a sum.

Product: result of multiplication (or sometimes division).
Sum: result of addition (or sometimes subtraction).