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

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

Grade:10

1 Answers

Chetan Mandayam Nayakar
312 Points
12 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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