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 $A - 3 B$

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Solution

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

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

$= (4 x^{2} + y^{2} - 6 x y) - (36 x^{2} + 9 y^{2} + 24 x y)$

$= - 32 x^{2} - 8 y^{2} - 30 x y$

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