Solve the differential equation $$(x+2)y''-xy'+(1-x^2)y=0 ; \quad X_0=1$$ using the power series method about the point $x_0=1$.
I get to this step after deriving the derivatives of the $\sum_0^\infty A_n(x-1)^n$ :
$$(1+(x-1))\left[ \sum_{n=2}^{\infty} (n(n-1)A_n(x-2)^{n-2}\right]-(1+(x-1))\left[\sum_{n=1}^{\infty} A_nn(x-1)^{n-1}\right] + (1-x^2)\left(\sum_{n=0}^{\infty}A_n(x-1)^n\right)$$
My problem is I don't understand how to distribute through the last piece $(1-x^2)$ as I do for the first piece where I substituted $(1+(x-1))$ to make it possible.