First, distribute each term within the parentheses:

(p-2c)(p+2c) = p^2 + 2cp - 2cp - 4c^2 = p^2 - 4c^2

(p-c)(p^2 + pc + c^2) = p^3 + p^2c + pc^2 - p^2c - pc^2 - c^3 = p^3 - c^3

Now subtract the second expression from the first:

(p^2 - 4c^2) - (p^3 - c^3) = p^2 - 4c^2 - p^3 + c^3

Rearranging terms, we get:

-p^3 + p^2 + c^3 - 4c^2

So, P(p-2c)(p+2c)-(p-c)(p^2+pc+c^2) simplifies to -p^3 + p^2 + c^3 - 4c^2.