I'm currently working on a problem which asks me to calculate the potential energy of a three spring system arranged in an equilateral triangle constrained to move in the x-y plane. As a consequence of solving the problem, I've come a cross a multi-term expression inside of a square root and am unsure how to approximate it to proceed further. I'm familiar with using Taylor Series to approximate series such as: $$(1+x)^\alpha = \sum_{n=o}^\infty{\frac{f^{(n)}(0)}{n!}x^n}$$
The current expression, however, is of the form: $$\sqrt{l^2 + 2l(x_2-x_1)+x_2^2+x_1^2-2x_1x_2+y_1^2+y_2^2-2y_1y_2}$$ where $l$ is a constant.
Is there an alternate form of Taylor Series I can use to address this? Or do I need to manipulate the expression further before I can apply approximation methods?