Simplify

(v) $(x + y) (2 x + y) + (x + 2 y) (x - y)$

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Solution

Step : Simplify the expression
$(x + y) (2 x + y) + (x + 2 y) (x - y)$
$= x (2 x + y) + y (2 x + y) + x (x - y) + 2 y (x - y)$
$= 2 x^{2} + x y + 2 x y + y^{2} + x^{2} - x y + 2 x y - 2 y^{2}$
$= 3 x^{2} + 4 x y - y^{2}$

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