SOLUTION: (ex+fy)(gx-hy) In the expression above, e,f,g, and h are non-zero constants and eh=fg. If eg=18 and fh= 50, what is the value of the coefficient of the xy term when the express

Algebra ->  Equations -> SOLUTION: (ex+fy)(gx-hy) In the expression above, e,f,g, and h are non-zero constants and eh=fg. If eg=18 and fh= 50, what is the value of the coefficient of the xy term when the express      Log On


   

Question 1090313: (ex+fy)(gx-hy)
In the expression above, e,f,g, and h are non-zero constants and eh=fg. If eg=18 and fh= 50, what is the value of the coefficient of the xy term when the expression is multiplied out and the like terms are collected?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
highlight%280%29 of course.
When you multiply two binomials, like %28ex%2Bfy%29 and %28gx-hy%29 you end up with 4 products.
In the case of %28ex%2Bfy%29%28gx-hy%29 , the four products are
%28ex%29%28gx%29 , %28ex%29%28-hy%29 , %28fy%29%28gx%29 , and %28fy%29%28-hy%29 .
Two of those will have x and y ,
and can be "simplified" into one term by "collecting like terms."
That term is
%28ex%29%28-hy%29%22%2B%22%28fy%29%28gx%29%22=%22
%28-eh%29%28xy%29%22%2B%22%28fg%29%28xy%29%22=%22
%28-eh%2Bfg%29%28xy%29 .
The coefficient of xy is %28-eh%2Bfg%29 ,
And if eh=fg , %28-eh%2Bfg%29=%28-fg%2Bfg%29=0 .