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Math Help - How to rearrange/manipulate algebraically?

  1. #1
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    How to rearrange/manipulate algebraically?

    This is a formula for chemistry, but I'm having trouble figuring out out it was rearranged. I'd love any help/steps/explanations on how this was rearranged!

    This is the first line:
    =\frac{h^2(n+1)^2\pi^2}{2mL^2}-\frac{h^2n^2\pi^2}{2mL^2}

    It was then manipulated to this:
    =(\frac{h^2\pi^2}{2mL^2})((n+1)^2-n^2)

    I'd appreciate any help!
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  2. #2
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    Re: How to rearrange/manipulate algebraically?

    Quote Originally Posted by maybealways View Post
    This is a formula for chemistry, but I'm having trouble figuring out out it was rearranged. I'd love any help/steps/explanations on how this was rearranged!

    This is the first line:
    =\frac{h^2(n+1)^2\pi^2}{2mL^2}-\frac{h^2n^2\pi^2}{2mL^2}

    It was then manipulated to this:
    =(\frac{h^2\pi^2}{2mL^2})((n+1)^2-n^2)

    I'd appreciate any help!
    They took out the highest common factor.
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  3. #3
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    Re: How to rearrange/manipulate algebraically?

    Factor out \frac{h^2 \pi^2}{2mL^2}.
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  4. #4
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    Re: How to rearrange/manipulate algebraically?

    Quote Originally Posted by maybealways View Post
    This is a formula for chemistry, but I'm having trouble figuring out out it was rearranged. I'd love any help/steps/explanations on how this was rearranged!

    This is the first line:
    =\frac{h^2(n+1)^2\pi^2}{2mL^2}-\frac{h^2n^2\pi^2}{2mL^2}
    Working from left to right, we see that there is a " h^2 in both terms. There is an (n+1)^2 in the first term but not the second. Likewise there is an n^2 in the second term but not the first. There is a \pi^2 in both terms. And, of course, there is 2mL^2 in the denominator of both terms. That means we can factor out \frac{h^2\pi^2}{2mL^2} leaving (n+1)^2- n^2. Hence:
    \frac{h^2\pi^2}{2mL^2}((n+1)^2- n^2).

    In fact, we could go a step further. Since (n+1)^2= n^2+ 2n+ 1, (n+1)^2- n^2= 2n+ 1 so we could write it as \frac{h^2\pi^2}{2mL^2}(2n+1).

    It was then manipulated to this:
    =(\frac{h^2\pi^2}{2mL^2})((n+1)^2-n^2)

    I'd appreciate any help!
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