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anonymous
 5 years ago
find the coefficient of x^4 in the expansion of (3x1)^11
anonymous
 5 years ago
find the coefficient of x^4 in the expansion of (3x1)^11

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0same as before \[\dbinom{11}{4}(3x)^4(1)^7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and what does the 11 over 4 part mean again?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[3^4=81\] \[(1)^7=1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to find \[\dbinom{11}{4}\]? if not i will be happy to show you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is called "eleven choose 4" the number of ways to choose 4 items out of 11.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0show please!! also why did u just do 3^4 isnt ther an x in there like 3x^4?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(3x)^4=3^4x^4\] and since you were asked for the coefficient that is the number you need to compute.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it is the whole thing raised to the power of 4, not just the x. that is it is \[(3x)^4\] not \[3x^4\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so there for it is 81x^4

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if i times it by the 1 like i was supposed to?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now to compute \[\dbinom{11}{4}\] yes there is a 81

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but you have to multiply by \[\dbinom{11}{4}\] which is easy enough to compute. i can show you step by step if you like

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok first of all a formula, although you don't really use it. the formula is \[\dbinom{n}{k}=\frac{n!}{k! (nk)!}\] here n = 11, k = 4 and nk=7 make a fraction. in the numerator put 4 numbers starting at 11 and counting down. in the denominator you put 4! to get \[\dbinom{11}{4}=\frac{11\times 10 \times 9\times 8}{4 \times 3\times 2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is my final answer 26730x^4?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now since this is a whole number , cancel first and multiply last! \[\frac{11 \times 10\times 9 \times 8}{4\times 3\times 2}={11\times 10\times 3}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{11}{4}=330\] \[330\times 81 \times 1=26730\] yes you got it!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thankyou so much!!!!!!! your awesome!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can i ask u about another??!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no problem. try \[\dbinom{10}{3}\] and convince yourself that it is the same as \[\dbinom{10}{7}\]because 3+7=10!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0find the coefficient of x^7 in the expansion of (2x5)^9

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok same idea. here n = 9, k = 7, nk=3 so the term with \[x^7\] will look like \[\dbinom{9}{7}(2x)^7(5)^3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my mistake. it will be \[\dbinom{9}{7}(2x)^7(5)^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0exponents have to add up to 9. would you like to try it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what would (2x)^7 be?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(2x)^7=2^7x^7\] so you will need to compute \[2^7\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats is easy, as is \[(5)^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0your real job is to compute \[\dbinom{9}{7}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes how do u do the 9 over 7 thging again?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{n}{k}=\frac{n!}{k! (nk)!}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here n = 9, k = 7 and nk=2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 9! over 7! times 2!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right. but don't forget to cancel away first because the entire denominator will cancel

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so 36 times 128 times 25

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now 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. \[\dbinom{9}{2}=\frac{9\times 8}{2}=9\times 4=36\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, 36 times 128 times 25 is it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh wait i got a different number than you. i got 115200

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe i put it in wrong.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no i think i am right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nah i put it in wrong!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0whew i was scared but it is late.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is that enough of this? or are there more?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i can help you with another if you like.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0one question quick.. the fianl answer is 115200x^7 rights?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nah its okay i will let u go! u were a great help! quick question .. ur suyper smart!! how old are u?!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0old as black pepper. have fun, and don't forget to convince yourself that \[\dbinom{10}{6}=\dbinom{10}{4}\]because 10=4+6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0awesome thanks!! haha
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