If $P = 7 x^{2} + 5 x y - 9 y^{2}, Q = 4 y^{2} - 3 x^{2}$ and $R = 4 x^{2} + x y + 5 y^{2}$ show that $P + Q + R = 8 x^{2} + 6 x y$

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Solution

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

Since,
$= P + Q + R$
$= 7 x^{2} + 5 x y - 9 y^{2} + 4 y^{2} - 3 x^{2} + 4 x^{2} + x y + 5 y^{2}$
$= 8 x^{2} + 6 x y$

Hence, proved.

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Similar questions

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

P = {3 x}^{2} + 7 x + 8, Q = {2 x}^{2} + x - 9

R = - {5 x}^{2} - 8 x + 1

P + Q + R = 0

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