Alternative proof:

Suppose, P = NP

P² = P(NP)

(subtracting (NP)²)

P² - (NP)² = P(NP) - (NP)²

(dividing both sides by P-(NP)):

P + (NP) =(NP)

since P = NP (initial assumption):

2*P = P

(dividing by P):

2 = 1

which is a contradiction, therefore P \not= NP