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Math Help - steps to simplify a problem

  1. #1
    Member integral's Avatar
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    steps to simplify a problem

    Hello, can someone show me the steps to simplifying:
    \Delta y=(t+\Delta t)^2 - t^2 + 8(t+\Delta t)-8t
    to
    \Delta y=2t(\Delta t) +(\Delta t)^2 +8 \Delta t

    please, thank you
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  2. #2
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    pickslides's Avatar
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    Hi there integral, all you need to do here is expand the expression and group the like terms.
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  3. #3
    Member integral's Avatar
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    \Delta y=(t+\Delta t)^2 -t^2 +8(t+\Delta t)-8t
    \Delta y=(t+\Delta t)(t+\Delta t) -t^2 +8(t+\Delta t)-8t
    \Delta y=t^2+t\Delta t+ (\Delta t(t))+\Delta t^2 -t^2 +8(t+\Delta t)-8t
    \Delta y=t^2+t\Delta t+ (\Delta t(t))+\Delta t^2 -t^2 +8\Delta t
    \Delta y=t\Delta t+ t\Delta t+\Delta t^2 +8\Delta t
    \Delta y=2(t\Delta t)+\Delta t^2 +8\Delta t


    right? I feel so dumb now. lol
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  4. #4
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    Looks ok, I would do it like this.

     \Delta y=(t+\Delta t)^2 - t^2 + 8(t+\Delta t)-8t

    Grouping

     \Delta y=[(t+\Delta t)^2 - t^2] + [8(t+\Delta t)-8t]

    Using the difference of 2 squares in the first part and expanding the 2nd part we get

     \Delta y=((t+\Delta t) - t)((t+\Delta t)+ t) + [8t+8\Delta t)-8t]

    And simplifying

     \Delta y=\Delta t (2t+\Delta t) + 8\Delta t

    And expanding again

     \Delta y=2t(\Delta t)+(\Delta t)^2 + 8\Delta t
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  5. #5
    Member integral's Avatar
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    That works as well (Thanks for the idea).
    Thank you
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