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Math Help - Special Product

  1. #1
    Newbie nickgc's Avatar
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    Special Product

    (ax+y)^2


    normally i would answer it as :
    (a^2)(x^2)+(y^2)

    but with special products it would be:
    (a^2)(x^2 ) + ( 2axy ) + ( y^2 )

    does that mean

    (a^2)(x^2)+(y^2)

    is wrong?
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  2. #2
    MHF Contributor
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    Re: Special Product

    What do you mean by special product?

    does that mean
    a2x2+y2
    is wrong?
    Yes. For any u and v, (u + v)^2 = u^2 + 2uv + v^2. Here u = ax and v = y; therefore, (ax + y)^2 = a^2x^2+2axy+y^2. You can check this by multiplying (ax+y)(ax+y) through explicitly, and also by substituting various numbers for a, x and y (e.g., a = x = y = 1).
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