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anonymous
 5 years ago
what is (2x+3) times itself 10 times?
anonymous
 5 years ago
what is (2x+3) times itself 10 times?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you mean \[(2x+3)^{10}\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0perhaps this is the answer or perhaps you are being asked to expand?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0alright well the original question is " find the coefficient of x^6 in the expansion of (2x+3)^10

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ahh that is a different story

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0because writing out the entire expansion is a pain.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Remember this formula for coefficient during expansion: 1 1 = Power 1 1 2 1 = Power 2 (Retain the 1st number, add 1st and 2nd number put as 2nd, retain 2nd number as 3rd) 1 3 3 1 = Power 3 (Retain the 1st number, add 1st and 2nd number put as 2nd, add 2nd and 3rd as 3rd, retain 3rd number as 4th) 1 4 6 4 1 = Power 4 1 5 10 10 5 1 = Power 5 Hence the coefficient of x³ is: 10*(2)³ *3²= 80 * 9 = 720 Note: Interestingly: (1) The terms for power 1 is 2, for power2 it is 3, for power n the terms are n + 2 (2) The sum of the coefficients for power 1 is: 1+1 = 2 = 2¹, for power 2, 1+2+1 = 4 = 2², power 3 is 1+3+3+1=2³,..., for power n, it is 2^n

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well thats what i have to do is find the coefficient of x^6 in the expansion of (2x+3)^10

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{10}{6}(2x)^6\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0^^ idk what that means....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The coefficient of x^5 is 8064 The x^6 has a coefficient of 13608

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{10}{6}=\frac{10\times 9 \times 8\times 7}{4\times 3\times 2}=210\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait wat that like wrong

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0maybe . i am tired. why? i thought it was 64*210=13440

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh carp. i am wrong. i forgot \[3^4\] that is there too!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0im sorry i have no idea what the H ur talking about

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0term with \[x^6\] looks like \[\dbinom{10}{6}(2x^6)(3^4)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you expand \[(a+b)^n\] the terms look like \[\dbinom{n}{k}a^kb^{nk}\] here n= 10 k=6 a = 2x b=3

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

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you get \[\dbinom{10}{6}(2x)^63^4\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\dbinom{10}{6}=210\] \[2^6=64\] \[3^4=81\] you have to multiply all this mess together. sorry i screwed up at the beginning.
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