SOLUTION: What is the term containing x6 in the expansion of (x+2y)10. Thanks

Algebra ->  Permutations -> SOLUTION: What is the term containing x6 in the expansion of (x+2y)10. Thanks      Log On


   

Question 1148573: What is the term containing x6 in the expansion of (x+2y)10.
Thanks
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Note: It is customary to use "^" (shift-6) to represent exponentiation. So

"What is the term containing x^6 in the expansion of (x+2y)^10"

instead of

"What is the term containing x6 in the expansion of (x+2y)10"

In the expansion, there are 10 identical factors of (x+2y).

To get a term containing x^6, you need to choose the "x" from 6 of the factors and the "2y" from the other 4 factors.

Each time you do that, the partial product is %28x%29%5E6%2A%282y%29%5E4.

The number of ways you can choose 6 of the 10 factors to contain "x" is "10 choose 6".

So the term containing x^6 in the expansion of (x+2y)^10 is