# Peskin QFT Textbook chapter 5 question

I'm trying to work through a calculation in the Peskin QFT textbook in chapter 5, specifically getting equation 5.10. They take two bracketed terms

$$4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)]$$

and

$$4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot k'+m_{\mu}^2)]$$

they set $m_e=0$ and take the dot product of these two to get

$${32e^4}[(p \cdot k)(p' \cdot k')+(p \cdot k')(p' \cdot k)+m^2_{\mu}(p \cdot p')]$$

When I do this I get

$$16[2(p' \cdot k)(p \cdot k')+2(k \cdot p)(p' \cdot k')-3(p' \cdot p)(k' \cdot k)-(p' \cdot p)m^2_{\mu}]$$

In this scattering problem the two incoming momenta are $p$ and $p'$ and outgoing $k$ and $k'$, so working in the COM frame I suspect there is a reduction you can make but I can't figure out what it is. Any help is appreciated!

$g^{\mu\nu} g_{\mu\nu}=4$. I have not seen your calculations, but my guess is you have taken this to be one.