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Math Help - How was this simplified?

  1. #1
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    How was this simplified?

    y^2 - 343 = x^{3} - 3(x^{2})(7) + 3(x)(49)-343
    to
    y^2 - 7^3 = (x-7)^3

    Is there a specific name for the second one? Could you please explain how to get from the first to the second.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by ericforman65 View Post
    y^2 - 343 = x^{3} - 3(x^{2})(7) + 3(x)(49)-343
    to
    y^2 - 7^3 = (x-7)^3

    Is there a specific name for the second one? Could you please explain how to get from the first to the second.
    Hi ericforman65,

    y^2-343=y^2-7^3 on the left.

    The right side was obtained from x^3-3x^3(7)+3x^2(49)+349 by recognizing the binomial expansion of (x-7)^3

    Remember the binomial theorem?

    (x-a)^3=x^3a^0-3x^2a^1+3x^1a^2-a^3

    Now, let a = 7

    (x-7)^3=x^3(7^0)-3x^2(7^1)+3x(7^2)-7^3

    (x-7)^3=x^3-3x^2(7)+3x(49)-343
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