# SOLUTION: how 5a+5b-2ab be the answer of the question b(5-a)-a(5-b)

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 614860: how 5a+5b-2ab be the answer of the question b(5-a)-a(5-b)Answer by Theo(3556)   (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.