Question 1013237: In the expansion of (2+x)^14 multiplied by (1+2/x)^14, find the coefficient of x^12. Found 2 solutions by stanbon, ikleyn:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! In the expansion of (2+x)^14 multiplied by (1+2/x)^14,
find the coefficient of x^12
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(2+x)^14*(1+(2/x))^14 = [(2+x)(1+(2/x))]^14 = [2+(4/x) + x + 2]^14
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= [x + 4/x + 4]^14
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etc.
Cheers,
Stan H.
You can put this solution on YOUR website! .
In the expansion of (2+x)^14 multiplied by (1+2/x)^14, find the coefficient of x^12.
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Apply the binomial formula to expand and . You will have
= * .
where are the binomial coefficients. (See the lessons
Introduction to Combinations and
Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion
in this site).
Now, when you open parentheses, cross-multiply the terms as it is required and collect the common terms,
you will see that comes from these and only from these terms:
* +
+ * +
+ * .
Thus the coefficient at will be
* + * + * .
Next substitute here = 1, = 1, = 1, calculate the rest of binomial coefficients and get the answer.
My part is to give you the general idea and the pivotal direction.
The rest is on you.
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