Why x2 +1 and x2 -1 are Not/Are Difference of Squares

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SUMMARY

The discussion clarifies that \(x^2 + 1\) is not a difference of squares, while \(x^2 - 1\) is indeed a difference of squares. The expression \(x^2 + 1\) can be factored using complex numbers as \( (x - i)(x + i) \), indicating that it does not fit the traditional definition of a difference of squares, which requires real factors. In contrast, \(x^2 - 1\) factors neatly into \((x - 1)(x + 1)\), confirming its status as a difference of squares.

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Abdullah Qureshi
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Explain why x2 +1 is not a difference of squares and x2 -1 is
 
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Oh, but it is ...

$x^2+1 = x^2 - (-1) = (x - i)(x + i)$
 

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