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  • 1 Post By v8archie
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August 5th, 2015, 04:13 PM   #1
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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
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August 5th, 2015, 04:18 PM   #2
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I guess..

(x^2+1)^2=(sqrt(2)*x)^2

x^2+1=+/-(sqrt(2)*x)
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August 5th, 2015, 06:07 PM   #3
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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.
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August 6th, 2015, 07:19 PM   #4
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(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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