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

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Solution

$I = (x + y) (2 x + y) I_{1} + (x + 2 y) (x - y) I_{2}$
$I_{1} = (x + y) (2 x + y)$
$= 2 x^{2} + x y + 2 x y + y^{2}$
$I_{1} = 2 x^{2} + 3 x y + y^{2}$
$I_{2} = (x + 2 y) (x - y)$
$= x^{2} - x y + 2 x y - 2 y^{2}$
$I_{2} = x^{2} + x y - 2 y^{2}$
$I = I_{1} + I_{2}$
$= 2 x^{2} + 3 x y + y^{2} + x^{2} + x y - 2 y^{2}$
$= 3 x^{2} + 4 x y - y^{2}$ .

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