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Math Help - transforming formulas

  1. #1
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    transforming formulas

    i got my formula to this point
    q=(x_1+x_2)^2-x_2^2+(x_1+x_3)^2-2x_3^2
    how from this form i can get it to be with another form
    in which we have 2(x_{1}+\frac{x_{2}}{2}+\frac{x_{3}}{2})^{2} member

    ?
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  2. #2
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    Re: transforming formulas

    Just multiply out both forms, then put them back together in pieces.
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  3. #3
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    Re: transforming formulas

    is there easiyer way?
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  4. #4
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    Re: transforming formulas

    It takes about 5 minutes. I just did it in less time than that.
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  5. #5
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    Re: transforming formulas

    are you still working on quadratic forms transgalactic?
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  6. #6
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    Re: transforming formulas

    The resulting formula doesn't appear that "nice", perhaps you could post the context in which you arrived at this question.
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  7. #7
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    Re: transforming formulas

    q= 2x_{1}^{2}+3x_{2}^{2}-x_{3}^{2}+2x_{1}x_{2}++2x_{1}x_{3}
    =x_{1}^{2}+x_{1}^{2}+3x_{2}^{2}-x_{3}^{2}+2x_{1}x_{2}+2x_{1}x_{3}
    =x_{1}^{2}+2x_{1}x_{2}+x_{1}^{2}+x_{2}^{2}+2x_{2}^  {2}-x_{3}^{2}+2x_{1}x_{3}=x_{1}^{2}+2x_{1}x_{2}+x_{1}^  {2}+x_{2}^{2}+2x_{2}^{2}-2x_{3}^{2}+x_{3}^{2}+2x_{1}x_{3}=
    =(x_{1}+x_{2})^{2}+x_{1}^{2}+x_{2}^{2}+2x_{2}^{2}-2x_{3}^{2}+2x_{1}x_{3}+x_{3}^{2}=

    =(x_{1}+x_{2})^{2}+x_{1}^{2}+x_{2}^{2}+2x_{2}^{2}-2x_{3}^{2}+(x_{1}+x_{3})^{2}-x_{1}^{2}=

    =(x_{1}+x_{2})^{2}+3x_{2}^{2}-2x_{3}^{2}+(x_{1}+x_{3})^{2}

    in my solution they from the start show this member
    2(x_{1}+\frac{x_{2}}{2}+\frac{x_{3}}{2})^{2}
    but i am not used to work with its formula
    i prefer the simple (a+b)^2 form

    you said that i should dissasmble every colse on both expressions and regroup

    but in the test i idont know the other expression
    so how to get this member into my formula
    ?
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  8. #8
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    Re: transforming formulas

    Quote Originally Posted by Deveno View Post
    are you still working on quadratic forms transgalactic?
    i am learning to a test so i try to solve every sort of question
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  9. #9
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    Re: transforming formulas

    Oh, you just need to use the distributive law:

    (a+b+c)^2=(a+b+c)(a+b+c)=a^2 +ab+ac+ba+b^2+bc+ca+cb+c^2=a^2+b^2+c^2+2(ab+bc+ac)
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  10. #10
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    Re: transforming formulas

    its not what i am asking.
    i want the from this form
    =(x_{1}+x_{2})^{2}+3x_{2}^{2}-2x_{3}^{2}+(x_{1}+x_{3})^{2}
    ill get
    (a+b+c)^2 member
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  11. #11
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    Re: transforming formulas

    That's not the same as your first post, so I'm afraid I'm unsure of what you're asking.
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