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 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^2-sqrt(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$$a^2-b^2=(a+b)(a-b)$$ The factorisation can be verified easily enough by expanding the brackets. Thanks from greg1313
 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^2-sqrt(2)*x+1) =(x^2+1+sqrt(2)*x)(x^2+1-sqrt(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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