SOLUTION: In the expression (ax + by)(cx - dy), a, b, c, and d are non-zero constants and ad = bc. If ac = 18 and bd = 50, what is the value of the coefficient of the xy term when the expres

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Question 1121228: In the expression (ax + by)(cx - dy), a, b, c, and d are non-zero constants and ad = bc. If ac = 18 and bd = 50, what is the value of the coefficient of the xy term when the expression is multiplied out and the like terms are collected?
Found 3 solutions by Boreal, ikleyn, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
(ax + by)(cx - dy)
acx^2+bc (xy)-ad (xy)-bd(xy)
This is equivalent to acx^2+ad (xy)-ad (xy)-bd(xy)=18x^2-50xy
-50 ANSWER

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
Why don't you multiply these expressions and collect like terms on your own?


It requires very elementary and basic skills only to do it.


If you do understand the meaning of the terms in this assignment, you must be able to do it on your own.


Ah!  In addition, you should be able to make elementary algebraic transformations ! 


So, EITHER you do it on your own OR you are in the wrong class.


Hint.   The answer is  0  (zero,  ZERO).


Be aware !   The solution by  @Boreal is   WRONG.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
In the expression (ax + by)(cx - dy), a, b, c, and d are non-zero constants and ad = bc. If ac = 18 and bd = 50, what is the value of the coefficient of the xy term when the expression is multiplied out and the like terms are collected?
After FOILING, you should get: %28ac%29x%5E2+-+%28ad+-+bc%29xy+-+%28bd%29y%5E2, and since ad = bc, then ad - bc = ad - ad, or bc - bc = 0, and so, we get: 0xy.

Therefore, coefficient on the xy term is 0. All other answers are WRONG, so IGNORE them.