Algebra I

what does factoring the sum or difference of two cubes mean

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asked by Allie
  1. It means using the handy known factorizations, as in

    (a^3+b^3) = (a+b)(a^2-ab+b^2)
    (a^3-b^3) = (a-b)(a^2+ab+b^2)

    Of course, only the sum is needed, since
    (a^3-b^3) = (a^3+(-b)^3)

    once you recognize the sum of two cubes, like

    125x^6+216/z^9
    where
    a = 5x^2
    b = 6/z^3
    just plug into the formula

    125x^6 + 216/z^9 = (5x^2+6/z)(25x^4-30x^2/z^3+36/z^6)

    so, it helps to know your cubes of small numbers, and watch for exponents which are multiples of 3.

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    posted by Steve

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