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Math Help - Sum of squares?

  1. #1
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    Sum of squares?

    Can someone please help me in solving this problem?

    [(1+t)^3 +3(1+t)^2 +2(1+t)] -6
    (1+t) -1

    So I know the sum a cube gives me (1+t)(1-t+t^2) for the first part of the problem, right?
    I am having difficulty with 3(1+t)^2 since I know there is no sum of squares; how am I supposed to factor/multiply this?

    Thanks for your help!
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  2. #2
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    \frac{(1+t)^{3}+3(1+t)^{2}+2(1+t)-6}{(1+t)-1}

    Expand out the numerator, and it is obvious the denominator is just t.

    The numerator simplifies and factors to t(t^{2}+6t+11)

    When we divide by t we get t^{2}+6t+11
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  3. #3
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    Would you mind showing me how you got t(t^2+6t+11) ?
    I keep getting way too many numbers that cannot be simplied or cancelled.
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  4. #4
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    *simplified, sorry
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  5. #5
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    The numerator simplifies to t^{3}+6t^{2}+11t

    Then, I just factored out a t.
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  6. #6
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    Quote Originally Posted by galactus View Post
    The numerator simplifies to t^{3}+6t^{2}+11t

    Then, I just factored out a t.
    I'm sorry but I really just don't understand this. Can you possibly show me what you did from the beginning of the problem? I just don't see how it comes out t^{3}+6t^{2}+11t
    Thank you, I really do appreciate your time and sorry for all the questions.
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  7. #7
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    It's nothing fancy, just expand it out.

    (1+t)^{3}=t^{3}+3t^{2}+3t+1

    3(1+t)^{2}=3t^{2}+6t+3

    2(1+t)=2+2t

    Put it all together:

    t^{3}+3t^{2}+3t+1+3t^{2}+6t+3+2+2t-6

    Now, add like terms and simplify:

    t^{3}+6t^{2}+11t

    There, that's all there is to it.
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