The problem wich I need an is idea to find an answer is below:
Prove that if the graph $H$ is obtained from the graph $G$ by subdividing the edge $uv$ then $$P_H(x)=P_G(x)+(x-1)P_{G-uv}(x)-P_{G-u}(x)-P_{G-v}(x)+P_{G-u-v}(x).$$
Subdividing edge $uv$ means adding vertex $t$, edges $tu$ and $tv$ morethere deleting $uv$.
I will be happy if you tell me about your knowledge.