HELP ME PLEASE! 36r^(7)s^(2) is the third term in the expansion of (r+s)^(9). True or False?

Question

campbell_st · Answer

using binomial expansion

$$^{9}C _{2}r^{9 - 2} s^2$$

just simplify

campbell_st · Answer

the powers of r and s are correct... you need to evaluate the combination 

$$^{9}C_{2} $$

jim_thompson5910 · Answer

Or you can use pascals triangle

Highlight (in yellow) the row that starts with 1, 9, etc and look for the third value (highlighted in red). This value is 36

jim_thompson5910 · Answer

So the coefficient is 36

anonymous · Answer

http://www.wolframalpha.com/input/?i=expand+%28r%2Bs%29^%289%29

anonymous · Answer

True

jim_thompson5910 · Answer

Then just realize that a pattern forms with the variable terms

1st term: r^9

2nd term: r^8s^1

3rd term: r^7s^2


Notice how the 'r' exponents count down while the 's' exponents count up


So the third term is indeed $\Large 36r^7s^2$