math

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I'm not exactly sure how to factor cubed roots:

8x^3 - 1 = (2x)^3 - 1

that's what i get; can it be simplified anymore?

  • math -

    i'm looking at another one, and i don't know where to start:

    x^3 - 2x^2 - 4x +8

    hmm, cause u can't pull and x out, no quadratic . . .???

  • math -

    your first one fits the pattern for the difference of cubes
    A^3 - B^3 = (A-B)(A^2 + AB + B^2)

    so (2x)^3 - 1 = (2x-1)(4x^2 + 2x + 1)

    test it by expanding my answer

    for you second one, try grouping
    I will get you started

    x^3 - 2x^2 - 4x +8
    = x^2(x-2) - 4(x-2)
    = ......

  • math -

    for function operations:
    If f(x) = x^2 -4 and g(x) = [square root of] (2x+4)

    g(f(a+2)) ---> then

    x^2 - 4 +2
    x^2 - x
    [square root of] (2(x^2 - 2) +4)

    = x [square root of] 2

    wher does 'a' come from?, but is that right?

  • math -

    the x has been replaced by a+2

    so since f(x) = x^2 -4 and g(x) = √ (2x+4)

    g(f(x)) = √(2(x^2-4) + 4)
    = √(2x^2 -4)

    then g(f(a+2))
    = √(2(a+2)^2 - 4)
    =√(2(a^2 + 4a + 4) - 4)
    = √(2a^2 + 8a + 4)

    check my algebra, sometimes without writing it down first, I tend to make errors while just working it out only on the screen.

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