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How to prove -(a+b) = (-a)+ (-b)

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jaxen28 | eNotes Newbie

Posted July 12, 2013 at 10:07 AM via web

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How to prove -(a+b) = (-a)+ (-b)

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mvcdc | Student, Undergraduate | (Level 1) Associate Educator

Posted July 12, 2013 at 10:16 AM (Answer #1)

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First of all, note that `-(a+b)` is equivalent to `-1*(a +b)` .

By the distributive property of multiplication, we have:

`(-1*a) + (-1*b)`

which can be simplified/written as:

`(-a) + (-b)` which is our desired expression.

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Another solution:

`-(a+b) = -a - b = -a + (-b) = (-a) + (-b)` again, the desired expression.

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