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  1. #1
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    Question Help with math problem

    ok so the problem is this :

    Let f(x) = (2x+4)^4

    Simplify ->
    f(x)-f(a)
    (x-a)

    Stated in words: f of x minus f of a, all divided by x minus a.

    so can anyone help me with this ASAP.
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  2. #2
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    Quote Originally Posted by bhaskar2 View Post
    ok so the problem is this :

    Let f(x) = (2x+4)^4

    Simplify ->
    f(x)-f(a)
    (x-a)

    Stated in words: f of x minus f of a, all divided by x minus a.

    so can anyone help me with this ASAP.
    f(x) = (2x+4)^4

    f(a) = (2a+4)^4

    f(x) - f(a) =

    (2x+4)^4 - (2a+4)^4 =

    [(2x+4)^2 + (2a+4)^2][(2x+4)^2 - (2a+4)^2] =

    [(2x+4)^2 + (2a+4)^2][(2x+4) + (2a+4)][(2x+4)-(2a+4)] =<br />

    [(2x+4)^2 + (2a+4)^2][2(x+a+4)][2(x-a)]<br />

    divide the last expression by x-a
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by bhaskar2 View Post
    ok so the problem is this :

    Let f(x) = (2x+4)^4

    Simplify ->
    f(x)-f(a)
    (x-a)

    Stated in words: f of x minus f of a, all divided by x minus a.

    so can anyone help me with this ASAP.
    (2x+4)^4-(2a+4)^4=((2x+4)^2-(2a+4)^2)((2x+4)^2+(2a+4)^2) by the difference of squares identity.

    (2x+4)^2-(2a+4)^2=((2x+4-(2a+4))(2x+4+2a+4)=4(x-a)(x+a+4) by difference of squares again.

    So the whole thing is \frac{4(x-a)(x+a+4)((2x+4)^2+(2a+4)^2)}{x-a}

    Cancel the x-a and then simplify.

    EDIT: Beat to it!
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