What is the fourth term of (x + y)8?

Question

anonymous · Answer

56x3y5
 		
36x3y5
 		
36x4y4
 		
56x5y3

campbell_st · Answer

for binomial expansions use the formula

$$(a + b)^n = ^{n}C _{r} a^{n-r}b^{r}$$ and the binomial will have n + 1 terms

so for the 4th term r = 3

the expansion is 

$$^{8}C _{3}x^{8-3}y^3$$

anonymous · Answer

b?

amistre64 · Answer

an easy check, for the exponents; is to start at the given exponent; 8 in this case

count down the number of terms it wants; 4 terms

8 7 6 5  ; the last number is going to be the exponent of your "front" term

anonymous · Answer

so is the answer 5?

amistre64 · Answer

5 is part of the answer; where does this 5 need to be located ?

anonymous · Answer

i dont know,where should it be?

amistre64 · Answer

on "the exponent of your 'front' term"

amistre64 · Answer

this isnt a solution of course, but a property that you can check to narrow the down the options

anonymous · Answer

ow,thanks,i get it now

amistre64 · Answer

good :)  the only vagueness might be in what consititues a front term

anonymous · Answer

from there,how do u narrow down to the real answer then?

amistre64 · Answer

numbers are read from left to right,  -->  in this direction

the front term that has any merit to me is the "x" since it is first in the original setup.

look for an x^5

anonymous · Answer

d?

amistre64 · Answer

d is nice yes

anonymous · Answer

is it a and b?

amistre64 · Answer

neither a nor b have a x^5 in them, so we can ignore them

anonymous · Answer

ow,i thought u meant, x raised to 5,

amistre64 · Answer

i did.  so x^3 does not fit the bill