ótt: \( \left(x^{2}+y^{2}\right)^{2}-(2 x y)^{2} \)

Did you know that this expression can be simplified using a well-known algebraic identity? It’s the difference of squares! The expression \( (a^2 - b^2) \) can be factored into \( (a - b)(a + b) \). Here, let \( a = (x^2 + y^2) \) and \( b = 2xy \). So, you can factor the original expression to yield \( ((x^2 + y^2) - (2xy))((x^2 + y^2) + (2xy)) \). This identity is quite handy in various fields like engineering and physics when you encounter problems involving circular shapes or wave interference patterns. For instance, simplifying complex expressions can make it easier to analyze systems or calculate particular outcomes—like finding the distance between two points in a circular path or understanding phase differences in wave phenomena. Never underestimate the power of algebra!