Show that $\sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k^4} = \sum_{k=1}^{2n} \frac{1}{k^4} - \frac{1}{8} \sum_{k=1}^{n} \frac{1}{k^4} $

Question

Show that $\sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k^4} = \sum_{k=1}^{2n} \frac{1}{k^4} - \frac{1}{8} \sum_{k=1}^{n} \frac{1}{k^4} $

I don't really know what to do, I tried expanding it and then seeing if I could group terms together however that didn't really help.

Any ideas?