Simplify: $(x + y)(x - y) + (x + y)^{2}$.

Simplify: $(x + y)(x - y) + (x + y)^{2}$.
  1. $2x^{2} + 2xy$
  2. $2x^{2} + y^{2}$
  3. $2x^{2} - 2xy$
  4. $2x^{2} + 2xy + 2y^{2}$

Solution

$(x^{2}-y^{2}) + (x^{2}+2xy+y^{2}) = 2x^{2} + 2xy$.

Asked in: IMO

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