Question

(p+q)2-(p-q)2 = ?
please solve this ....

Answer 1

(P+Q)² - (P-Q)²  =  ?

   Left Hand Side LHS  is in the form  A²  - B²  =  (A + B ) ( A - B )

here  A =  P+Q    B is P-Q

So LHS  =  ( P + Q  + P - Q )  [ P + Q  - (P - Q) ]
  
             =  (2 P ) ( p + Q - P + Q )  =  2 P * 2 Q
 
            = 4 P Q
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We can also do this by expanding (P+Q)²

LHS  =  P² + Q² + 2 PQ - [ P² + Q² - 2 PQ ]

         = P² + Q² + 2 PQ - P² - Q² + 2 PQ

         = 4 PQ

First method is more intelligent method, second method is more hard work, basic principles method.

Answer 2

(p+q)2-(p-q)2
= 2p + 2q -2p +2q
= 4q