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Question 614860: how 5a+5b-2ab be the answer of the question b(5-a)-a(5-b)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the problem is to simplify b(5-a) - a(5-b)
distribute the multiplication to get:"
b*5 - b*a - a*5 - a*(-b)
this simplifies further to:
b*5 - b*a - a*5 + a*b
this can be written as:
5b - ab - 5a + ab
the - ab and the + ab cancel out and you are left with:
5b - 5a
in confirmed the answer is correct by substituting values at random for a and b and then solving with the original equation and the final equation to see if the results match.
since they do, i assume i did it correctly.
example:
let a = 7 and b = 20
these number were chosen at random.
using the original expression of b(5-a)-a(5-b), I get:
20(5-7) - 7(5-20) becomes:
20(-2) - 7(-15) which becomes:
-40 - (-105) which becomes:
-40 + 105 which becomes:
65
using the final expression of 5b - 5a, I get:
5*20 - 5*7 becomes:
100 - 35 which becomes:
65
i get the same answer whether i use the original equation or the final equation so i'm fairly confident the answer is correct.
i also went back and double checked my arithmetic and it checks out.
the difficulty in a problem such as this is the double negatives when you are multiplying -a(5-b)
b(5-a) is easy enough.
that give you 5b - ab
-a(5-b) is more difficult.
that give you -a*5 + -a*-b which results in:
-5a + ab
the other way of treating this is as follows:
-a(5-b) is equivalent to:
- (a*(5-b)) which then becomes:
- (5a - ab) which then becomes:
- 5a + ab
either way, that last ab is a plus and it cancels out the earlier - ab.
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