If then show that P(x) P(y) = P(x + y) = P(y) P(x).

Given.

We need to prove that P(x)P(y) = P(x + y) = P(y)P(x).

First, we will evaluate P(x)P(y).

Now, we will evaluate P(y)P(x).

Thus, P(x)P(y) = P(x + y) = P(y)P(x).