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Math Help - Factoring by Grouping

  1. #1
    mmsan
    Guest

    Factoring by Grouping

    note: x^2 means x ( or whatever variable) to the power of 2
    p^2-q^2+r^2-2pr

    factor by grouping ( or any other method)
    i've tried to factor it into this format: (x-y+z)(x-y-z), but i can't seem to do it. the answer key says that the answer is (p-r+q)(p-r-q), but I don't understand how they got to it.
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  2. #2
    Super Member

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    Hello, mmsan!

    Factor: . p^2 - q^2 + r^2 -2pr

    It's a sneaky one . . .

    Group it like this: . (p^2 - 2pr + r^2) - q^2

    Factor: . (p - r)^2 - q^2\;\;\Leftarrow
    difference of squares!

    Factor again: . [(p - r) - q][(p - r) + q] \;=\;(p - r - q)(p - r + q)

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