SOLUTION: Factoirse x^2- (( a+b)^2+a^2/a^2+ab) x+1

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Question 1025959: Factoirse x^2- (( a+b)^2+a^2/a^2+ab) x+1
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
 
x%5E2-+%28%28%28a%2Bb%29%5E2%2Ba%5E2%29%2F%28a%5E2%2Bab%29%29x%2B1

x%5E2-+%28%28%28a%2Bb%29%5E2%2Ba%5E2%29%2F%28a%28a%2Bb%29%29%29x%2B1 

Since a+b appears twice, let c = a+b 

x%5E2-+%28%28c%5E2%2Ba%5E2%29%2F%28ac%29%29x%2B1

Get a least common denominator of ac



Factor out 1%2Fac

expr%281%2Fac%29%28%28ac%29x%5E2-%28a%5E2%2Bc%5E2%29%5E%22%22x%2Bac%29

So we try to factorize the trinomial like this,
breaking up %28ac%29x%5E2 as the product of ax and cx:



It doesn't take too much thinking to know that we
must fill in the blank spaces with c and a to
cause the product to be ac



And if we find the outer and inner products, we
find that we get -aČ-bČ which is -(aČ+bČ).

So that is the correct factorization.  All that's
left is to substitute (a+b) for c and simplify:

  

Removing the inner parentheses we have:

 

Edwin