Add $4 x^{2} - 7 x y + 4 y^{2} - 3$ ,
$5 + 6 y^{2} - 8 x y + x^{2}$

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Solution

$4 x^{2} - 7 x y + 4 y^{2} - 3 + 5 + 6 y^{2} - 8 x y + x^{2}$
$= 5 x^{2} + 10 y^{2} - 15 x y + 2$
$= 5 x^{2} - 5 x y - 10 x y + 10 y^{2} + 2$
$= 5 x (x - y) - 10 y (x - y) + 2$
$= 5 (x - 2 y) (x - y) + 2$

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