anonymous
  • anonymous
what is (2x+3) times itself 10 times?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
x= 5
anonymous
  • anonymous
you mean \[(2x+3)^{10}\]?
anonymous
  • anonymous
perhaps this is the answer or perhaps you are being asked to expand?

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anonymous
  • anonymous
alright well the original question is " find the coefficient of x^6 in the expansion of (2x+3)^10
anonymous
  • anonymous
ahh that is a different story
anonymous
  • anonymous
because writing out the entire expansion is a pain.
anonymous
  • anonymous
Remember this formula for co-efficient 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
  • anonymous
well thats what i have to do is find the coefficient of x^6 in the expansion of (2x+3)^10
anonymous
  • anonymous
ohh kk
anonymous
  • anonymous
\[\dbinom{10}{6}(2x)^6\]
anonymous
  • anonymous
^^ idk what that means....
anonymous
  • anonymous
The coefficient of x^5 is -8064 The x^6 has a coefficient of -13608
anonymous
  • anonymous
\[\dbinom{10}{6}=\frac{10\times 9 \times 8\times 7}{4\times 3\times 2}=210\]
anonymous
  • anonymous
\[2^6=64\]
anonymous
  • anonymous
wait wat that like wrong
anonymous
  • anonymous
maybe . i am tired. why? i thought it was 64*210=13440
anonymous
  • anonymous
oh carp. i am wrong. i forgot \[3^4\] that is there too!
anonymous
  • anonymous
im sorry i have no idea what the H ur talking about
anonymous
  • anonymous
term with \[x^6\] looks like \[\dbinom{10}{6}(2x^6)(3^4)\]
anonymous
  • anonymous
if you expand \[(a+b)^n\] the terms look like \[\dbinom{n}{k}a^kb^{n-k}\] here n= 10 k=6 a = 2x b=3
anonymous
  • anonymous
ohhh okay haha thanks
anonymous
  • anonymous
so you get \[\dbinom{10}{6}(2x)^63^4\]
anonymous
  • anonymous
\[\dbinom{10}{6}=210\] \[2^6=64\] \[3^4=81\] you have to multiply all this mess together. sorry i screwed up at the beginning.

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