Simplify Expression and Find Product of a*b + 15m + 11n + 8

[ParisSpart]

for which value of a the expression write a*m*b+15*m+11*n+8 can be written into a product
of something(with m)*something (with n)

i can think how to find the product of this expression

 

[HallsofIvy]

Two points- first the problem does NOT ask you to find the product- it asks you to find a so that it can be written as a product. Second, you have written the problem incorrectly. That first term "amb" does not mmae any sense. You could just combine "b" into "a". Further a product of a "something (with n)" and "something (with m)" must have a term in which m and n themselves are mutiplied. I believe the problem was "a*m*n", not "a*m*b".

"Something with n" times "something with m" would be of the form (pm+ q)(sn+ t) for some numbers p, q, s, and t. Multiplying that, (ps)mn+ (pt)m+ (qs)n+ qt. For that to be amn+ 15m+ 11n+ 8 we must have ps= a, pt= 15, qs= 11, and qt= 8. If we divide qs= 11 by qt= 8, the "q"s cancel and we get t/s= 11/8. If we divide ps= a by pt= 15, the "p"s cancel and we get s/t= a/15. From t/s= 11/78 we get s/t= 8/11 and so must have a/15= 8/11.

 

[ParisSpart]

i forgot to say that the expression is (a*m*n+15*m+11*n+8)^2 but its says that this a that we found its not correct...

 

[ParisSpart]

and its 1/(this expression)...

 

[ParisSpart]

where is the wrong?

 

[haruspex]

ps= a, pt= 15, qs= 11, and qt= 8. ... a/15= 8/11.

a = ps = (pt)(qs)/(qt) = 15*11/8