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Simplify: (3x+5)^3-3x(x^2-1)

  • Math -

    If you know the quick expansion of

    (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^2, then your expression is

    = (3x)^3 + 3(3x)^2(5) + 3(3x)(5)^2 + 5^3 - 3x^3 + 3x
    = 27x^3 + 135x^2 + 225x + 125 - 3x^3 + 3x
    = 24x^3 + 135x^2 + 228x + 125



    (here is a quick way to see if your answer is correct.
    pick any simple value for x
    say x=1
    original value = (8^3) - 3(0) = 512
    answer value = 24 + 135 + 228 + 125 = 512
    let x=0
    original = 5^3 + 0 = 125
    new one = 0+0+0+125 = 125

    Even though this does not absolutely prove that our answer is right, the probability that I am right is very very high.
    It would definitely prove my answer would be wrong if the two results would not be the same.)

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