Approximation to simplify an equation

Question

I found this approximation on the solution of a book. $$\left(1+\frac{\Delta^2}{d^2}\right)^{\frac {-3} {2} }+\left(1-\frac{\Delta^2}{d^2}\right)^{-2}= \left(1-\frac{3}{2}\frac{\Delta^2}{d^2}+...\right)+\left(1+\frac{2\Delta^2}{d^2}+...\right)$$ Can anybody help me explain this approximation technique?

Answer 1

MacLaurin expansion $$(x+1)^{-3/2} \approx 1 -\frac{3 x}{2}+\frac{15 x^2}{8} -\frac{35 x^3}{16}+\ldots$$

And $$(1 - x)^{-2}\approx 1 + 2 x + 3 x^2 + 4 x^3 + \ldots$$