SOLUTION: can somebody please help me understand how to go about this question: Find the term not involving y in the expansion of (1/y^3+y^2)^5. Please help!! Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can somebody please help me understand how to go about this question: Find the term not involving y in the expansion of (1/y^3+y^2)^5. Please help!! Thank you.      Log On


   

Question 155827: can somebody please help me understand how to go about this question:
Find the term not involving y in the expansion of (1/y^3+y^2)^5. Please help!! Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A general expansion would be,
%28a+%2B+b%29%5E5+=+a%5E5%2B5a%5E4b+%2B+10a%5E3b%5E2+%2B10a%5E2b%5E3+%2B5ab%5E4+%2B+b%5E5
Let a=y%5E-3 and b=y%5E2, the term not involving y will have y canceling out in the numerator and denominator.
a%5E2=y%5E-6
b%5E3=y%5E6
a%5E2b%5E3=y%5E-6%2Ay%5E6=y%5E%28-6%2B6%29=1
That's the third term of the expansion, 10a%5E2b%5E3=10%281%29=10.