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Math Help - factoring cubed function

  1. #1
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    factoring cubed function

    (x+(DELTAX))^3

    i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
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  2. #2
    MHF Contributor

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    Quote Originally Posted by maybnxtseasn View Post
    (x+(DELTAX))^3

    i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
    It is factored. Do you mean you want to multiply it?

    One way: (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2
    = x^2+ 2x\Delta x+ (\Delta x)^2k

    and then (x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2 = (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2) = x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2
    = x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3

    Quicker way: if you know the general formula (a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3, use that with a= x and b= \Delta x to get the same thing.
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