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Math Help - Expanding Binomials

  1. #1
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    Expanding Binomials

    Find the expansion of (r + 4)</I>3


    I have the hardest time ever with this topic. I need a good, clear explanation on how to expand these (for someone who's an apparent math moron).
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  2. #2
    MHF Contributor red_dog's Avatar
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    Do you mean (r+4)^3 ?

    (a+b)^3=a^3+3a^2b+3ab^2+b^3
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  3. #3
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    Hello, BlueStar!

    Find the expansion of: . (r + 4)^3
    The very least you could do is mutliply it out . . .


    First, find (r +4)^2

    . . (r + 4)^2 \;=\;(r+4)^2 \;=\;r^2 + 4r +4r + 16 \;=\;r^2 + 8r + 16


    The multiply by another (r+4)

    . . (r+4)(r^2 + 8r + 16) \;=\;r^3 + 8r^2 + 16r + 4r^2 + 32r + 64 \;=\;\boxed{r^3 + 12r^2 + 48r + 64}


    If you are seeking a shortcut to this type of multiplication,
    . . then you want the Binomial Theorem (or Binomial Expansion).
    Perhaps someone will explain it to you . . . or not.

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