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

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Solution

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

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

$= 2 x^{2} + x y + 2 x y + y^{2} + x^{2} - x y + 2 x y - 2 y^{2}$

$= (2 + 1) x^{2} + (1 + 2 - 1 + 2) x y + (1 - 2) y^{2}$

$= 3 x^{2} + 4 x y - y^{2}$

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