Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.)
(x + 5y)^10, n = 4
A. 210x^6y^4
B. 15,000x^7y^3
C. 210x^6y^4
D. 9,765,625y^10
E. 5040x^6y^4

- anonymous

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- anonymous

n=10? I believe???
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- anonymous

nevermind... term in the expansion

- anonymous

which is a different variable rth term of expansion

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## More answers

- anonymous

I guess I understand how to write it all out just not how to simplify it correctly to get a condensed answer like the ones they provide

- anonymous

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54_bi_theor.htm Look at example 8... if you have problems I'll do it out for you

- amistre64

pascals triangle

- anonymous

Ha ha I'm on that site right now trying to work it out lol Does it matter though if it's rth term or nth term?

- anonymous

doesn't matter coz thats just a variable

- amistre64

1
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1
1,6,15,20,15,6,1
1,7,21,35,35,21,7,1
1,8,28,56,70,56,28,8,1
1,9,36,84,126,126,84,36,9,1
1,10,45,120,210, ....

- anonymous

well if you are following the site, the rth term is 4, the nth term is 10

- amistre64

120 (x^7) (y^3)

- anonymous

answer is b though

- amistre64

120 (x^7) ((5y)^3)

- amistre64

120.125 x^7 y^3
15000 x^7 y^3

- amistre64

BBBBBBBBBB

- anonymous

\[{10 \choose 4 }=210\]
4th term is
\[210 x^6 (5y)^4\]

- anonymous

of course i could be wrong. the 'n=4' is not clear.

- amistre64

lol..... im prolly wrong :)

- anonymous

wow ok the answer I got isn't even close to any of these.... I got 100800x^7125y^3....not quite sure what id id wrong

- amistre64

the 4th term is 120 x^7 y^3 as a standard... tehn you have to account for the coeefs in the original problem....namely the +5 attached to the y

- amistre64

120 x^7 (5y)^3

- amistre64

120.125 x^7 y^3
15000 x^7 y^3 :)

- anonymous

oh ok makes sense ok Can I try another one on my own and have you check it?

- amistre64

sure; but you can check it with pascals triangle; i posted that first to like half the 10th spot ;)

- anonymous

ok :)

- anonymous

ok the problem is:
Find the specified nth term in the expansion of the binomial. (Write the expansion in descending powers of x.)
(x - 2y)^12, n = 6
I got 760x^7y^5
which is definitly not one of my answer choices....

- amistre64

at 6 eh
12 11 10 9 8 7
x^6 y^6 is gonne be the variable answers

- amistre64

you got any with ony an x^6 y^6 as an asnswer?

- anonymous

oh it's cause I used the 12 instead of the six let me try it again....

- amistre64

ack..you were right with the x and y lol...i lost count :)

- amistre64

x^7 y^5 is the 6th term

- anonymous

oh ok so I was right now....idk how I got the 760.... cause that's nowhere close to their choices

- amistre64

lol..... which choice has the right x and y parts?

- amistre64

narrow it down if its multiple choice ;)

- anonymous

- 25,344, but that just doesn't seem right to me oh well I guess

- amistre64

well lets play detective shall we :)
is the - part correct?
-2^5 = a negative right? so i believe the negative is right...
if its got the right x and y parts, then its a sure shot

- anonymous

ok well thank you very much!

- anonymous

Do you know the binomial theorem?! It's quite easy to do it using this theorem.

- anonymous

learning it I think i just have to keep practicing using cause I get numbers mixed up and stuff

- anonymous

I see.

- anonymous

ya it's weird I can find the x and y parts but the number before I somehow lkeep messing up

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