Add $2 x^{2} - 8 x y + 7 y^{2} - 8 x y^{2}, 2 y^{2}, 6 x y^{2} - y^{2} + 3 x^{2}, 4 y^{2} - x y - x^{2} + x y^{2}$ .

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Solution

$(2 x^{2} - 8 x y + 7 y^{2} - 8 x y^{2}) + (2 y^{2}) + (6 x y^{2} - y^{2} + 3 x^{2}) + (4 y^{2} - x y - x^{2} + x y^{2})$

$\Rightarrow$ $2 x^{2} - 8 x y + 7 y^{2} - 8 x y^{2} + 2 y^{2} + 6 x y^{2} - y^{2} + 3 x^{2} + 4 y^{2} - x y - x^{2} + x y^{2}$
Rearranging and combining the like terms,
$\Rightarrow$ $(2 x^{2} + 3 x^{2} - x^{2}) + (- 8 x y - x y) + (7 y^{2} + 2 y^{2} - y^{2} + 4 y^{2}) + (- 8 x y^{2} + 6 x y^{2} + x y^{2})$

$\Rightarrow$ $4 x^{2} - 9 x y + 12 y^{2} - x y^{2}$

$\Rightarrow$ $4 x^{2} + 12 y^{2} - 9 x y - x y^{2}$

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