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Expression and product

  1. May 22, 2013 #1
    for which value of a the expression write a*m*b+15*m+11*n+8 can be written into a product
    of something(with m)*something (with n)

    i can think how to find the product of this expression
     
  2. jcsd
  3. May 22, 2013 #2

    HallsofIvy

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    Two points- first the problem does NOT ask you to find the product- it asks you to find a so that it can be written as a product. Second, you have written the problem incorrectly. That first term "amb" does not mmae any sense. You could just combine "b" into "a". Further a product of a "something (with n)" and "something (with m)" must have a term in which m and n themselves are mutiplied. I believe the problem was "a*m*n", not "a*m*b".

    "Something with n" times "something with m" would be of the form (pm+ q)(sn+ t) for some numbers p, q, s, and t. Multiplying that, (ps)mn+ (pt)m+ (qs)n+ qt. For that to be amn+ 15m+ 11n+ 8 we must have ps= a, pt= 15, qs= 11, and qt= 8. If we divide qs= 11 by qt= 8, the "q"s cancel and we get t/s= 11/8. If we divide ps= a by pt= 15, the "p"s cancel and we get s/t= a/15. From t/s= 11/78 we get s/t= 8/11 and so must have a/15= 8/11.
     
  4. May 22, 2013 #3
    i forgot to say that the expression is (a*m*n+15*m+11*n+8)^2 but its says that this a that we found its not correct...
     
  5. May 22, 2013 #4
    and its 1/(this expression)....
     
  6. May 22, 2013 #5
    where is the wrong?
     
  7. May 22, 2013 #6

    haruspex

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    a = ps = (pt)(qs)/(qt) = 15*11/8
     
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