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February 3rd, 2014, 05:47 PM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  An expression x^2 + (3y + 5)x + 2(y + 3)(y + 1)
In the expression x^2 + (3y + 5)x + 2(y + 3)(y + 1), what is the reason behind 2(y + 3) + (y + 1) = 3y + 5? What is the relationship between the coefficient of x, (3y + 5), and the three products 2(y + 3)(y + 1)?

February 3rd, 2014, 08:51 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,852 Thanks: 1570 
The correct equation is (y + 3) + 2(y + 1) = 3y + 5. That equation is clearly valid and explains why x² + (3y + 5)x + 2(y + 3)(y + 1) factorizes as (x + y + 3)(x + 2(y + 1)). 

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