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Simplify (3x-2)^3 - (4x+5)^2

Can you show it step-by-step please

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asked by Kimmie
  1. You need the Binomial Theorem:
    (a+b)^n = a^n + n a^(n-1) b + ...
    So, you have

    (3x-2)^3
    = (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3
    = 27x^3 - 54x^2 + 36x - 8

    (4x+5)^2
    = (4x)^2 + 2(4x)(5) + 5^2
    = 16x^2 + 40x + 25

    Subtract them to get

    27x^3 - 70x^2 - 4x - 33

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    posted by Steve

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