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.
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.