Question 881051: Factor: 35+2m -m^2
My solution:
= -(m^2 -2m -35)
= - ( (m-7)(m+5) )
then I get confused.
To get rid of the minus, don't I apply it across both sets of parentheses?
That would be = (7-m)(-5 -m)
but the actual answer is (7-m)(5 + m)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 35+2m -m^2 = -(m^2 -2m -35) = - ( (m-7)(m+5) ) as you said.
But that minus sign is a (-1) multiplied times ( (m-7)(m+5) ) .
You have 3 factors to be multiplied in any order:
- ( (m-7)(m+5) ) = (-1) ( (m-7)(m+5) ) = ((-1)(m-7))(m+5) = (-m+7)(m+5) = (7-m)(m+5)
You can write it many different ways, but I do not like to write more parentheses than needed.
I prefer -(m-7)(m+5) or (-1)(m-7)(m+5) , but it is a question of taste, or of whatever you are going to do next with the resulting expression.
You are thinking about the distributive property, where a number is multiplied times a sum, as in
a(b+c)=ab+ac ,
but in this case the minus sign is a (-1) multiplied times a product, not times a sum. It's the case of
a(bc)=(ab)c , and we know those brackets do nothing but waste ink, so we just write it as abc.
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