SOLUTION: Find the term that is independent of x in the expansion of (2+2/x^2)(x-3/x)^6.

Question 1170639: Find the term that is independent of x in the expansion of (2+2/x^2)(x-3/x)^6.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Find the term that is independent of in the expansion of
Formula to use
th term=

For :

th term=th term=

For the th term involving :

then

For the th term involving :

The constant term in the expansion of is:

← answer

check with expanded form:

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The expansion of the second factor will be in the form

When that is multiplied by , we will get constant partial products from two places: and

So the constant term in the final expansion will be

So we need to calculate the coefficients of the constant and x^2 terms, C and D.

Then

ANSWER: -810

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