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Thread: Help simplifying

  1. #1
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    Help simplifying

    I can't seem to simplify this correctly


    $\displaystyle 20(5-\frac{t}{4})-2(5-\frac{t}{4})^2 + t(5-\frac{t}{4}) $
    Can someone show me step by step how i break this down?
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  2. #2
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    Quote Originally Posted by el123 View Post
    I can't seem to simplify this correctly


    $\displaystyle 20(5-\frac{t}{4})-2(5-\frac{t}{4})^2 + t(5-\frac{t}{4}) $
    Can someone show me step by step how i break this down?
    Hi

    You can see that $\displaystyle 5-\frac{t}{4}$ can be factored

    $\displaystyle 20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(20 - 2 \left(5-\frac{t}{4}\right) + t\right)$

    $\displaystyle 20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(20-10+\frac{t}{2}+t\right)$

    $\displaystyle 20\left(5-\frac{t}{4}\right)-2\left(5-\frac{t}{4}\right)^2 + t\left(5-\frac{t}{4}\right) = \left(5-\frac{t}{4}\right)\left(10+\frac{3t}{2}\right)$
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  3. #3
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    ok i orginally wrote it wrong but i get what t6 do , but now im stuck on this part

    $\displaystyle -2(5-\frac{t}{4})^2$

    I keep getting

    $\displaystyle -2(25 -10t+\frac{t^2}{4}$

    which gives
    $\displaystyle -50 + 20t+\frac{t^2}{8}$


    But it doesn't fit into what my answer should be, i think i expanded that wrong.
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  4. #4
    MHF Contributor Matt Westwood's Avatar
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    Quote Originally Posted by el123 View Post
    ok i orginally wrote it wrong but i get what t6 do , but now im stuck on this part

    $\displaystyle -2(5-\frac{t}{4})^2$

    I keep getting

    $\displaystyle -2(25 -10t+\frac{t^2}{4}$

    which gives
    $\displaystyle -50 + 20t+\frac{t^2}{8}$


    But it doesn't fit into what my answer should be, i think i expanded that wrong.
    Like this:

    $\displaystyle -2\left({5-\frac{t}{4}}\right)^2$

    $\displaystyle = -2 \left({5^2 - 2 \times 5 \left({\frac{t}{4}}\right) + \left({\frac{t}{4}}\right)^2}\right)$

    $\displaystyle = -2 \left({5^2 - \frac {5t} 2 + \frac{t^2}{16}}\right)$
    Last edited by Matt Westwood; Sep 12th 2009 at 04:53 AM. Reason: hadn't finished
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