# Binomial expansion terms

• Nov 28th 2008, 05:02 AM
Greengoblin
Binomial expansion terms
When we expand a binomial, $(x+y)^n$ I understand how the coefficient of $x^r$ will be $^nC_r$, but not why the terms group together as they do in the form $x^{n-r}y^r$.

Why is this the case and not $x^ry^r$ for example?
• Nov 28th 2008, 05:18 AM
mr fantastic
Quote:

Originally Posted by Greengoblin
When we expand a binomial, $(x+y)^n$ I understand how the coefficient of $x^r$ will be $^nC_r$, but not why the terms group together as they do in the form $x^{n-r}y^r$.

Why is this the case and not $x^ry^r$ for example?

Try expanding using concrete value of n like n = 2, n = 3, n = 4. Then you should see that the sum of the powers has to add up to n.
• Nov 28th 2008, 05:55 AM
Greengoblin
Thanks I've tried expanding for n=2,3,4, using the formula, and doing algebraically, and got the expected expressions in both cases, but still can't see why the powers of x and y in each term must add to n.