cancell common factors

Question

p³ - PQ²
--------- Divided by
(P+Q)²

Apparently the answer is

P(P-Q)
--------- Divided by
P+Q

But how? - What I was thinking
P-P (P-Q), (P+Q)
------------------ Divided by
(P+Q)

which is

P-P (P-Q)
------------Divided by
(P+Q)

How is it that 4p's become 2 p's? Please answer step by step.

Answer 1

$$\require{cancel}\frac{P^3-PQ^2}{(P+Q)^2}=\frac{P(P^2-Q^2)}{(P+Q)^2}=\frac{P(P-Q)\cancel{(P‌​+Q)}}{(P+Q)\cancel{(P+Q)}}=\frac{P(P-Q)}{P+Q}$$