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If I want to complete the square with

[itex](-x^{2}-4x+3)[/itex] I would write

[itex](-x^{2}-4x+(...) +3 - (...)) = (-x^{2}-4x+4+3-4) = (-x^{2}-4x+4-1) = (x^{2}+4x-4) - 1[/itex]

Why does adding the parentheses to separate the -1 change all the signs. I understand it has something to do with factoring out a negative, but how exactly?

I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus?

[itex](-x^{2}-4x+3)[/itex] I would write

[itex](-x^{2}-4x+(...) +3 - (...)) = (-x^{2}-4x+4+3-4) = (-x^{2}-4x+4-1) = (x^{2}+4x-4) - 1[/itex]

Why does adding the parentheses to separate the -1 change all the signs. I understand it has something to do with factoring out a negative, but how exactly?

I thought adding parentheses to a series of additions and/or subtractions is simply an associative property. Signs don't need to change in associate property, so why would they change when adding parentheses to separate the -1 when completing the square for an integration problem in calculus?

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