August 5th, 2015, 04:13 PM  #1 
Senior Member Joined: May 2012 Posts: 205 Thanks: 5  factor
How does (x^2+sqrt(2)*x+1)(x^2sqrt(2)*x+1) follow from: (x^2+1)^2(sqrt(2)*x)^2 
August 5th, 2015, 04:18 PM  #2 
Senior Member Joined: May 2012 Posts: 205 Thanks: 5 
I guess.. (x^2+1)^2=(sqrt(2)*x)^2 x^2+1=+/(sqrt(2)*x) 
August 5th, 2015, 06:07 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,691 Thanks: 2670 Math Focus: Mainly analysis and algebra 
More or less. It's just the difference of two squares$$a^2b^2=(a+b)(ab)$$ The factorisation can be verified easily enough by expanding the brackets. 
August 6th, 2015, 07:19 PM  #4 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
(x^2+sqrt(2)*x+1)(x^2sqrt(2)*x+1) =(x^2+1+sqrt(2)*x)(x^2+1sqrt(2)*x) =((x^2+1)+(sqrt(2)*x))((x^2+1)(sqrt(2)*x)) Now, try using what v8archie told you with a=x^2+1 and b=sqrt(2)*x. 

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