Question 1148573
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Note: It is customary to use "^" (shift-6) to represent exponentiation.  So<br>
"What is the term containing x^6  in the expansion of (x+2y)^10"<br>
instead of<br>
"What is the term containing x6  in the expansion of (x+2y)10"<br>
In the expansion, there are 10 identical factors of (x+2y).<br>
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.<br>
Each time you do that, the partial product is {{{(x)^6*(2y)^4}}}.<br>
The number of ways you can choose 6 of the 10 factors to contain "x" is "10 choose 6".<br>
So the term containing x^6 in the expansion of (x+2y)^10 is<br>
{{{(C(10,6))*((x)^6)*((2y)^4) = 210(x^6)(16y^4) = 3360x^6y^4}}}<br>