Consider the ordinary generating function $e(x)=\sum_{n\geq0}e(n)x^n$ for the number $e(n)$ of partitions of the integer $n$ into even parts. Express $e(x)$ as a product of simple generating functions.
So I know that the number of partitions of $n$ into even parts is given by $$\prod_{i\geq0}\frac{1}{1-x^{2i}}$$ but I'm unsure how to express this as a product of simple generating functions, any help would be appreciated.