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Math Help - factorizing question

  1. #1
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    factorizing question

    how do you factorize this question: 49-(x+1)^2

    i would have known how to do it, if the 49 was on the other side: (x+1)^2 - 49
    then you would just find the square root of 49 which is 7
    and make (x+1+7)(x+1-7) and simplify.
    but i don't know how to do it with the 49 on the other side.

    Thanks for the help sorry its an easy question lol this is still advanced for me
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  2. #2
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    As long as it is subtraction, there is little concern where the constant should stand. You would the exactly the same and get:
    49-(x+1)^2 = (7-(x+1))*(7+(x+1))

    Be careful not to miss a bracket:
    (7-(x+1)) does not equal (7-x+1).
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  3. #3
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    so how do you simplify this: (7-(x+1))*(7+(x+1))
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  4. #4
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    (7-(x+1))*(7+(x+1))

    You could get rid of the internal brackets:
    (7-(x+1))*(7+(x+1)) = (7-x-1)(7+x+1)=(6-x)(x+8)=-(x-6)(x+8).
    You could get rid of these brackets aswell, but it cannot get simpler than that.
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  5. #5
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    The easiest way might be to take the negative sign outside...

    49-(x+1)^2 = -[(x+1)^2 -49]=-[(x+8)(x-6)]=(x+8)(6-x)

    In the last step take the negative to one of the factors.
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