Question

what is the coefficient of the fourth term in the expansion of (a-4b)^9?

Answer 1

heya

Answer 2

hi, can you help me?

Answer 3

sure

Answer 4

binomial expansion i see

Answer 5

\[\large (a-4b)^9=\sum_{k=0}^{9} \binom{k}{9}a^k(-4b)^{9-k}=\sum_{k=0}^{9} \binom{k}{9}(-4)^{9-k}a^kb^{9-k}\]
Now, the fourth term is where k=5 whether you go forward or backward so we plug it in out expression for the (n-1)th term without the a's and b's:
\[\binom{9}{5}(-4)^4\]
Now chug this in your calculator. :)

Answer 6

yeah that's right^

Answer 7

put into your calc: (9C5)(-4^4)

Answer 8

so when they're asking for the 4th term - it's really the 5th term?

Answer 9

it's the 4th term

Answer 10

OMG I made a big mistake!
It should have been k=3, not k=5.
In any case, if they're asking for the mth term, plug in m-1. :)

Answer 11

you made me look bad for saying "yup he's right"

Answer 12

>_>_<_>_>

Answer 13

haha yeah i got confused for a second! alright, thank you so much :)

Answer 14

sheesh it's not that hard...i'm doing this in C2 AS edexcel lol

Answer 15

which exam u doing?

Answer 16

algebra 2/trigonometry regents june 2011

Answer 17

it's (9C3)(a^(9-3))(-4b^(0+3))

Answer 18

he's totally wrong btw listen to me and give me a medal honey :]

Answer 19

you have to cube the -4 also

Answer 20

and the b

Answer 21

and a^9

Answer 22

The OP was asking for the coefficient, not the term.

Answer 23

oh right

Answer 24

so cube the -4 lol which gives you -64

Answer 25

and you guys get it easy in the States anyway, it's multi choice lol

Answer 26

i'm living in hong kong btw

Answer 27

wbu guys?

Answer 28

lol no, not everything is multiple choice.

Answer 29

i'm doing the SAT for the first time, didn't prepare yet lol

Answer 30

i know i'm late :S

Answer 31

the answer choices are nothing to what you guys gave me - ;

Answer 32

i have 14 other exams to tend to afte rthe SATs.. >_>

Answer 33

what are the multi answers?

Answer 34

-5376 , -336, 336, and 5376

Answer 35

oh pellet i think it's -5376

Answer 36

lol did i say pellet? i was meant to say shi... you know lol

Answer 37

it's definitely -5376, sorry

Answer 38

forgot the (9C3)

Answer 39

so plug into your calc (9C3)(-4^3)

Answer 40

and you get -5376

Answer 41

medal pl0x :]