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Thread: Help with binomial expansions

  1. #1
    AJD
    AJD is offline
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    Unhappy Help with binomial expansions

    Is there a quick way to expand: (3x + 5)(x - 7)?

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  2. #2
    Master Of Puppets
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    Using a computer will be quite quick.

    Its not a tricky one though, have you seen the F.O.I.L method?
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by AJD View Post
    Is there a quick way to expand: (3x + 5)(x - 7)?

    FOIL will be quickest but you can also use the distributive property
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  4. #4
    MHF Contributor
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    Quote Originally Posted by AJD View Post
    Is there a quick way to expand: (3x + 5)(x - 7)?

    This is a good example where you may say "and" instead of "plus".

    $\displaystyle (2+3)(1+5)=5(6)=30$

    We may also write

    $\displaystyle (2+3)(1+5)=2(1+5)$ and $\displaystyle 3(1+5)$ or $\displaystyle 1(2+3)$ and $\displaystyle 5(2+3)$

    which is

    $\displaystyle 2(1)$ and $\displaystyle 2(5)$ and $\displaystyle 3(1)$ and $\displaystyle 3(5)$

    $\displaystyle 2+10+3+15=30$

    The whole is the sum of the parts

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    $\displaystyle (3x+5)(x-7)=3x(x-7)+5(x-7)=3x(x)+3x(-7)+5(x)+5(-7)$

    which is the 3x multiplied by both in the 2nd brackets and 5 by both in the 2nd brackets.
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