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Value of an Expression

Let A = 3y2 +...

Question

$Let A = 3 y^{2} + 9 x - 3 x^{2}, B = 6 x^{2} - 2 y^{2} + 3 x, C = 9 x^{2} - 3 x y - y^{2} . Find A + B - C.$

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Solution

Given:
$A = 3 y^{2} + 9 x - 3 x^{2}$
$B = 6 x^{2} - 2 y^{2} + 3 x$
$C = 9 x^{2} - 3 x y - y^{2}$
$A + B = (3 y^{2} + 9 x - 3 x^{2}) + (6 x^{2} - 2 y^{2} + 3 x)$
(Grouping the like terms together)
$= (3 y^{2} - 2 y^{2}) + (9 x + 3 x) + (- 3 x^{2} + 6 x^{2})$
$= y^{2} + 12 x + 3 x^{2}$

Now subtracting C from (A+B),
$(A + B) - C = (y^{2} + 12 x + 3 x^{2}) - (9 x^{2} - 3 x y - y^{2})$
$= y^{2} + 12 x + 3 x^{2} - 9 x^{2} + 3 x y + y^{2}$
(Grouping the like terms together)
$= (y^{2} + y^{2}) + (3 x^{2} - 9 x^{2}) + (3 x y) + (12 x)$
$= 2 y^{2} - 6 x^{2} + 3 x y + 12 x$

On rearranging the terms we get,
$A + B - C = - 6 x^{2} + 3 x y + 12 x + 2 y^{2}$

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Let A = 3 y^{2} + 9 x - 3 x^{2}, B = 6 x^{2} - 2 y^{2} + 3 x, C = 9 x^{2} - 3 x y - y^{2} . Find A + B - C.

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