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I cannot figure out how the left side is converted to the right side...can someone please explain? I have tried some factoring methods but it doesn't give me the right side.

$$ e^{2x^2} + 2e^{x^2} + 2 = (e^{x^2} + 1)^2 + 1$$

I tried Wolfram but all it says is True, doesn't show me how left side becomes right side.

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Hint: do you see how the squared quantity multiplies out? If so, can you use that to factor the left hand side and get the result? –  Amzoti Nov 28 '12 at 4:16
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The equality is incorrect as stated. The lefthand side is "$+1$" larger than the righthand side. –  Austin Mohr Nov 28 '12 at 4:26
    
I put in a correction as an edit on both the title and result, but it has yet to be approved. –  Amzoti Nov 28 '12 at 4:32

3 Answers 3

up vote 1 down vote accepted

let $ a=e^{x^2} $, Then the statement becomes $ a^2+2a+2=(a+1)^2+1 $, subtracting 1 from both sides gives $a^2+2a+1=(a+1)^2$, which is an obvious statement, thus it must be true

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it looks like completing the square from what I can tell. Using variable "a" makes it much clearer to see how they factored using complete the square method. Thanks everyone! –  Raynos Nov 28 '12 at 4:22

Friend: Wolfram don`t lies. It's true!

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I think it's much clearer to see how the right side becomes the left. To do this, you just multiply out $(e^{x^2} + 1)(e^{x^2}+1)$.

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