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Grade 10Algebra

Can anyone explain me whats Sophie German Identity?? ??

Profile image of Sathya
14 Years agoGrade 10
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1 Answer

Profile image of Chetan Mandayam Nayakar
14 Years ago

The Sophie Germain Identity states that:

a^4 + 4b^4 = (a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab)

One can prove this identity simply by multiplying out the right side and verifying that it equals the left. To derive the factoring, first completing the square and then factor as a difference of squares:

\begin{align*}a^4 + 4b^4 & = a^4 + 4a^2b^2 + 4b^4 - 4a^2b^2 \\& = (a^2 + 2b^2)^2 - (2ab)^2 \\& = (a^2 + 2b^2 - 2a...

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