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