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Math Help - a^2 + b^2

  1. #1
    Junior Member phgao's Avatar
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    a^2 + b^2

    Is there anything you can do to a^2 + b^2 i.e can you factorise it somehow or is it only a^2 - b^2 you can factorise?

    Thanks!
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  2. #2
    Member jacs's Avatar
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    a - b = (a - b)(a + b) the difference of two squares

    one way of manipulating a + b which comes in handy for some applications (especally in parametrics) is this


    a + b = (a + b) - 2ab
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  3. #3
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    Quote Originally Posted by phgao
    Is there anything you can do to a^2 + b^2 i.e can you factorise it somehow or is it only a^2 - b^2 you can factorise?
    It can be written as a^2 + b^2 = (a+ib)(a-ib) which quickly leads you to the fact that the product of sums of two squares is again a sum of two squares: (a^2+b^2)(c^2+d^2) = (ac-bd)^2 + (ad+bc)^2.
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  4. #4
    Junior Member phgao's Avatar
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    Ah, thanks to both of you. Especially the factorization with i .
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