What should be added to x²+ 6xy+y² to obtain 2x²+3xy?

Let p should be added.
Then according to question,
x²+xy+y²+p=2x²+3xy
⇒ p = 2x² + 3xy -(x²+xy+y²)
⇒ p = 2x² + 3xy -x²+xy-y²
⇒ p = 2x²- x² – y² + 3xy – xy
⇒ p = x² – y² +2xy
Hence, x²-y²+2xy should be added.

Class 7 Maths Chapter 12 Exercise 12.2

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