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Math Help - expanding this

  1. #1
    Member
    Joined
    Jun 2009
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    108

    expanding this

    i am having trouble expanding this expression.

    (y-2)(y-4)(y+1)

    can you please help?
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  2. #2
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
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    Wellington
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    927
    Hello,
    you could expand it as follows :

    (y - 2)(y - 4)(y + 1)

    Let's first expand (y - 2)(y - 4). This is done by distributing :

    (y - 2)(y - 4) = y \times y + y \times (-4) + (-2) \times y + (-2) \times (-4) = y^2 - 4y - 2y + 8 = y^2 - 6y + 8

    Therefore :

    (y - 2)(y - 4)(y + 1) = (y^2 - 6y + 8)(y + 1)

    Now apply the distributive law again :

    (y^2 - 6y + 8)(y + 1) = y^2 \times y + y^2 \times 1 + (-6y) \times y + (-6y) \times 1 + 8 \times y + 8 \times 1 = y^3 + y^2 -6y^2 -6y + 8y + 8 = y^3 - 5y^2 + 2y + 8

    Finally :

    (y - 2)(y - 4)(y + 1) = y^3 - 5y^2 + 2y + 8

    Does this help ?

    PS : since I'm in a good mood I'll give you a nice website to check your results (if you don't know it already). It is called Wolfram Alpha, and you can type in what you want it to do (like "expand/factor/simplify [expression]", "solve [equation]"), and it will most likely do it correctly.
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