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August 9th, 2015, 11:38 AM  #1 
Newbie Joined: Aug 2015 From: UK Posts: 9 Thanks: 0  Factorizing 16x^481y^4, why is the answer written like this?
I can understand how the answer is reached: square root both sides to make it (4x^2 + 9y^2) (4x^2  9y^2) Then factorize the latter brackets to get a final answer of (4x^2 + 9y^2) (2x + 3y) (2x  3y) Is the reason for not factorizing further with the first set of brackets because the answer would be the same for both brackets as (2x + 3y) (2x + 3y) or (2x  3y) (2x  3y)? Why is this done? I want to be extra sure about the rules on this. 
August 9th, 2015, 01:11 PM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 
$4x^2+9y^2$ is not factorable over the real numbers

August 9th, 2015, 08:40 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2215  
August 10th, 2015, 10:00 AM  #4  
Senior Member Joined: Feb 2010 Posts: 711 Thanks: 147  Quote:
You can perform the same operation to both sides of a relation ($\displaystyle =,<,$ etc.) As has been pointed out, what you want in this problem is to apply the wellknown factor pattern called difference of squares $\displaystyle x^2y^2=(x+y)(xy)$  

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