Question

find the coefficient of x^4 in the expansion of (3x-1)^11

Answer 1

same as before
\[\dbinom{11}{4}(3x)^4(-1)^7\]

Answer 2

and what does the 11 over 4 part mean again?

Answer 3

\[3^4=81\]
\[(-1)^7=-1\]

Answer 4

do you know how to find \[\dbinom{11}{4}\]? if not i will be happy to show you.

Answer 5

it is called "eleven choose 4" the number of ways to choose 4 items out of 11.

Answer 6

show please!! also why did u just do 3^4 isnt ther an x in there like 3x^4?

Answer 7

\[(3x)^4=3^4x^4\] and since you were asked for the coefficient that is the number you need to compute.

Answer 8

it is the whole thing raised to the power of 4, not just the x. that is it is
\[(3x)^4\] not \[3x^4\]

Answer 9

so there for it is -81x^4

Answer 10

if i times it by the -1 like i was supposed to?

Answer 11

now to compute \[\dbinom{11}{4}\]
yes there is a -81

Answer 12

but you have to multiply by \[\dbinom{11}{4}\] which is easy enough to compute. i can show you step by step if you like

Answer 13

thatd be great!

Answer 14

ok first of all a formula, although you don't really use it.
the formula is
\[\dbinom{n}{k}=\frac{n!}{k! (n-k)!}\]
here n = 11, k = 4 and n-k=7
make a fraction. in the numerator put 4 numbers starting at 11 and counting down.
in the denominator you put 4!
to get
\[\dbinom{11}{4}=\frac{11\times 10 \times 9\times 8}{4 \times 3\times 2}\]

Answer 15

is my final answer -26730x^4?

Answer 16

now since this is a whole number , cancel first and multiply last!

\[\frac{11 \times 10\times 9 \times 8}{4\times 3\times 2}={11\times 10\times 3}\]

Answer 17

?

Answer 18

\[\dbinom{11}{4}=330\]
\[330\times 81 \times -1=-26730\]
yes you got it!

Answer 19

thankyou so much!!!!!!! your awesome!

Answer 20

can i ask u about another??!

Answer 21

no problem. try
\[\dbinom{10}{3}\] and convince yourself that it is the same as \[\dbinom{10}{7}\]because 3+7=10!

Answer 22

sure ask away.

Answer 23

find the coefficient of x^7 in the expansion of (2x-5)^9

Answer 24

ok same idea. here n = 9, k = 7, n-k=3 so the term with \[x^7\] will look like
\[\dbinom{9}{7}(2x)^7(-5)^3\]

Answer 25

oops typo sorry

Answer 26

n-k=2!

Answer 27

my mistake.
it will be \[\dbinom{9}{7}(2x)^7(-5)^2\]

Answer 28

exponents have to add up to 9. would you like to try it?

Answer 29

so what would (2x)^7 be?

Answer 30

\[(2x)^7=2^7x^7\] so you will need to compute \[2^7\]

Answer 31

thats is easy, as is \[(-5)^2\]

Answer 32

your real job is to compute \[\dbinom{9}{7}\]

Answer 33

yes how do u do the 9 over 7 thging again?

Answer 34

\[\dbinom{n}{k}=\frac{n!}{k! (n-k)!}\]

Answer 35

here n = 9, k = 7 and n-k=2

Answer 36

so 9! over 7! times 2!

Answer 37

right. but don't forget to cancel away first because the entire denominator will cancel

Answer 38

the answer is 36?

Answer 39

exactly!

Answer 40

so 36 times 128 times 25

Answer 41

so 25200x^7?

Answer 42

now i show you the easy way. first of all 7+2=9 so it is easier to compute \[\dbinom{9}{2}\]
so we work as before. make a fraction. in the numerator put to numbers starting at 9
in the denominator put 2. we get the answer right away.
\[\dbinom{9}{2}=\frac{9\times 8}{2}=9\times 4=36\]

Answer 43

good!!

Answer 44

yes, 36 times 128 times 25 is it.

Answer 45

oh wait i got a different number than you. i got 115200

Answer 46

maybe i put it in wrong.

Answer 47

no i think i am right.

Answer 48

nah i put it in wrong!

Answer 49

whew i was scared but it is late.

Answer 50

is that enough of this? or are there more?

Answer 51

you have to go?

Answer 52

i can help you with another if you like.

Answer 53

one question quick.. the fianl answer is 115200x^7 rights?

Answer 54

final answer yes.

Answer 55

nah its okay i will let u go! u were a great help! quick question .. ur suyper smart!! how old are u?!

Answer 56

old as black pepper. have fun, and don't forget to convince yourself that \[\dbinom{10}{6}=\dbinom{10}{4}\]because 10=4+6

Answer 57

awesome thanks!! haha