# Binomial expansion terms

• Nov 28th 2008, 04:02 AM
Greengoblin
Binomial expansion terms
When we expand a binomial, \$\displaystyle (x+y)^n\$ I understand how the coefficient of \$\displaystyle x^r\$ will be \$\displaystyle ^nC_r\$, but not why the terms group together as they do in the form \$\displaystyle x^{n-r}y^r\$.

Why is this the case and not \$\displaystyle x^ry^r\$ for example?
• Nov 28th 2008, 04:18 AM
mr fantastic
Quote:

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

Why is this the case and not \$\displaystyle 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, 04:55 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.