Question

What is the fourth term in the expansion of (x + 2y)^8?

a. 336x^5y^3

b. 448x^5y^3

c. 1120x^4y^4

d. 1680x^4y^4
Please explain too! :)

Answer 1

http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=6767c31553b5f2c292b426c97a9b6013&title=Binomial%20Expansion%20Calculator&theme=blue&i0=x%20-%202y&i1=5&podSelect=&includepodid=Input&includepodid=Result

Answer 2

I don't know how to read that.. haha so what's the answer? and can you please explain it? :) Hi @jim_thompson5910 and @ParthKohli thanks for comin to help :)

Answer 3

The k+1th term of (A+B)^n is

(n C k)*(A)^(n-k)*(B)^k


For example, the 3rd term of (x+2y)^8 is when k+1 = 3 ---> k = 2

So

(n C k)*(A)^(n-k)*(B)^k

(8 C 2)*(x)^(8-2)*(2y)^(2)

28x^6*(4y^2)

112x^6y^2

which means that the third term is 112x^6y^2


Use this idea to find the fourth term (so when k = 3)

Answer 4

hopefully the notation I used isn't too cluttered and it makes sense

Answer 5

so is the fourth term 448x^5y^3??? or is it something else??? idk!!!

Answer 6

you nailed it, very nice

Answer 7

Yay!! thanks :)

Answer 8

the answer is b then??

Answer 9

yes

Answer 10

cool beans :)Thanks!!!

Answer 11

yw