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

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Solution

Use the Distributive Property of Multiplication
Consider $(x + y) (2 x + y) + (x + 2 y) (x - y)$
So, $(x + y) (2 x + y) + (x + 2 y) (x - y)$
$= x (2 x + y) + y (2 x + y) + x (x - y) + 2 y (x - y) = 2 x^{2} + x y + 2 x y + y^{2} + x^{2} - x y + 2 x y - 2 y^{2} = 3 x^{2} + 4 x y - y^{2}$
Hence, $(x + y) (2 x + y) + (x + 2 y) (x - y)$ is $3 x^{2} - y^{2} + 4 x y$

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