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anonymous

  • 5 years ago

what is (2x+3) times itself 10 times?

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  1. anonymous
    • 5 years ago
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    x= 5

  2. anonymous
    • 5 years ago
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    you mean \[(2x+3)^{10}\]?

  3. anonymous
    • 5 years ago
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    perhaps this is the answer or perhaps you are being asked to expand?

  4. anonymous
    • 5 years ago
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    alright well the original question is " find the coefficient of x^6 in the expansion of (2x+3)^10

  5. anonymous
    • 5 years ago
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    ahh that is a different story

  6. anonymous
    • 5 years ago
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    because writing out the entire expansion is a pain.

  7. anonymous
    • 5 years ago
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    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

  8. anonymous
    • 5 years ago
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    well thats what i have to do is find the coefficient of x^6 in the expansion of (2x+3)^10

  9. anonymous
    • 5 years ago
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    ohh kk

  10. anonymous
    • 5 years ago
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    \[\dbinom{10}{6}(2x)^6\]

  11. anonymous
    • 5 years ago
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    ^^ idk what that means....

  12. anonymous
    • 5 years ago
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    The coefficient of x^5 is -8064 The x^6 has a coefficient of -13608

  13. anonymous
    • 5 years ago
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    \[\dbinom{10}{6}=\frac{10\times 9 \times 8\times 7}{4\times 3\times 2}=210\]

  14. anonymous
    • 5 years ago
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    \[2^6=64\]

  15. anonymous
    • 5 years ago
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    wait wat that like wrong

  16. anonymous
    • 5 years ago
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    maybe . i am tired. why? i thought it was 64*210=13440

  17. anonymous
    • 5 years ago
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    oh carp. i am wrong. i forgot \[3^4\] that is there too!

  18. anonymous
    • 5 years ago
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    im sorry i have no idea what the H ur talking about

  19. anonymous
    • 5 years ago
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    term with \[x^6\] looks like \[\dbinom{10}{6}(2x^6)(3^4)\]

  20. anonymous
    • 5 years ago
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    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

  21. anonymous
    • 5 years ago
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    ohhh okay haha thanks

  22. anonymous
    • 5 years ago
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    so you get \[\dbinom{10}{6}(2x)^63^4\]

  23. anonymous
    • 5 years ago
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    \[\dbinom{10}{6}=210\] \[2^6=64\] \[3^4=81\] you have to multiply all this mess together. sorry i screwed up at the beginning.

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