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Math Help - Trinomial product shortcut

  1. #1
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    Trinomial product shortcut

    Hello, I am having trouble with this problem:

    Find the product of (x+y-2) and (x+y+2)

    Now, obviously I can use the, so to speak, "old fashion" way by foiling it. But they say in the solution that I can use a special product and rewrite it as:

    [(x+y)-2][(x+y)+2]

    And furthermore be written as:

    (x+y)^2-2^2

    Could someone please explain how they are doing this?

    Thank you very much.
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  2. #2
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    Re: Trinomial product shortcut

    Quote Originally Posted by Bashyboy View Post
    Hello, I am having trouble with this problem:
    Find the product of (x+y-2) and (x+y+2)
    Just do it: (x+y-2)(x+y+2)=(x)(x)+(x)(y)+(x)(2)+(y)(x)+(y)(y)+(y)(2  )+(-2)(x)+(-2)(y)+(-2)(2)~.
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  3. #3
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    Re: Trinomial product shortcut

    Quote Originally Posted by Bashyboy View Post
    Hello, I am having trouble with this problem:

    Find the product of (x+y-2) and (x+y+2)

    Now, obviously I can use the, so to speak, "old fashion" way by foiling it. But they say in the solution that I can use a special product and rewrite it as:

    [(x+y)-2][(x+y)+2]

    And furthermore be written as:

    (x+y)^2-2^2

    Could someone please explain how they are doing this?

    Thank you very much.
    You should know that \displaystyle (a - b)(a + b) = a^2 - b^2 from the Difference of Two Squares rule.

    Here they have let \displaystyle a = x + y and \displaystyle b = 2.
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