Algebra

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How can you determine if a polynomial is the difference of two squares? I think that if the polynomial is x^2-64 that this is a polynomial that is a difference of two squares because if you factor it out you would get
(x+8)(x-8).
If the 64 in my example were positive would there still be a difference between two squares since x^2 and 64 both are squared numbers?

  • Algebra -

    No, when it says difference, it needs the single - sign.
    (a-b)(a+b) = a^2 + ab -ab - b^2 = a^2-b^2
    but
    (a+b)(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2 which is no good

  • Algebra -

    Oh and x^2+64
    solve x^2 + 0x + 64 = 0
    x = [-0 +/- sqrt (0 -256) / 2
    x = +/- sqrt (-256) /2
    x = +/- 8 i
    so
    x*2+64 = (x-8i)(x+8i)
    In other words there is no real number solution, You need the sqrt of -1 or "i"

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