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Math Help - 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
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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".

    (2+3)(1+5)=5(6)=30

    We may also write

    (2+3)(1+5)=2(1+5) and 3(1+5) or 1(2+3) and 5(2+3)

    which is

    2(1) and 2(5) and 3(1) and 3(5)

    2+10+3+15=30

    The whole is the sum of the parts

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    YZZZZZ
    YZZZZZ
    YZZZZZ


    (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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