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Binomial Expansion

  1. May 8, 2008 #1
    (1+4x)^7 i need to fully expand.

    il use (4c0) for 4 Ncr 0.


    (4c0)1^4 + (4c1) 1^3 + 4x + (4c2) 1^2 4x^2 + (4c3) 1 + 4x^3 +
    (4c4) 4x^4.

    this gives the completely wrong answer.

    i know this isn't the way your meant to do it, but i can't remember what's wrong here.

    can someone tell me how to do this.. thanks :P
     
  2. jcsd
  3. May 8, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, it does! For one thing you have have only 4th power while your problem says 7th powers. Is one of those a typo? The second difficulty is that "(4c1)1^3+ 4x". the 3rd power of 1 should be multiplied by the "4x", not added: (4c1)1^3(4x). Finally, it is "4x" that should be to each power, not just "x".
    (1+ 4x)^4= (4c0)1^4+ (4c1)1^3(4x)+ (4c2)1^2(4x)^2+ (4c3)1(4x)^3+ (4c4)(4x)^4

     
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