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

Sathya , 13 Years ago
Grade 10
anser 1 Answers
Chetan Mandayam Nayakar

Last Activity: 13 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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