If $A = 4 x^{2} + y^{2} - 6 x y; B = 3 y^{2} + 12 x^{2} + 8 x y; C = 6 x^{2} + 8 y^{2} + 6 x y$
Find $2 A + B$

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Solution

Given that,
$A = 4 x^{2} + y^{2} - 6 x y$
$B = 3 y^{2} + 12 x^{2} + 8 x y$
$C = 6 x^{2} + 8 y^{2} + 6 x y$

$2 A + B = 2 (4 x^{2} + y^{2} - 6 x y) + (3 y^{2} + 12 x^{2} + 8 x y)$

$= (8 x^{2} + 2 y^{2} - 12 x y) + (12 x^{2} + 3 y^{2} + 8 x y)$

$= 20 x^{2} + 5 y^{2} - 4 x y$

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