If $A = 7 x^{2} + 5 x y - 9 y^{2}, B = - 4 x^{2} + x y + 5 y^{2}$ and $C = 4 y^{2} - 3 x^{2} - 6 x y$ then show that $A + B + C = 0$

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Solution

$A + B = 7 x^{2} + 5 x y - 9 y^{2} - 4 x^{2} + x y + 5 y^{2}$

$= 3 x^{2} + 6 x y - 4 y^{2}$

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

$= 0$

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Similar questions

P = 7 x^{2} + 5 x y - 9 y^{2}, Q = 4 y^{2} - 3 x^{2}

R = 4 x^{2} + x y + 5 y^{2}

P + Q + R = 8 x^{2} + 6 x y

3 x^{2} + 5 x y - 4 y^{2} + x^{2} - 8 x y - 5 y^{2}

4 x^{2} - 3 x y - 9 y^{2}

3 x^{2} - 4 y^{2} + 5 x y + 20

- x^{2} - y^{2} + 6 x y + 20

3 x^{2} + 5 x y - 4 y^{2} + x^{2} - 8 x y - 5 y^{2}

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