Subtract $5 x^{2} - 4 y^{2} + 6 y - 3$ from $7 x^{2} - 4 x y + 8 y^{2} + 5 x - 3 y$

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Solution

Given: Subtract $5 x^{2} - 4 y^{2} + 6 y - 3$ from $7 x^{2} - 4 x y + 8 y^{2} + 5 x - 3 y$
$= 7 x^{2} - 4 x y + 8 y^{2} + 5 x - 3 y - (5 x^{2} - 4 y^{2} + 6 y - 3)$
$= 7 x^{2} - 4 x y + 8 y^{2} + 5 x - 3 y - 5 x^{2} + 4 y^{2} - 6 y + 3$
$= (7 x^{2} - 5 x^{2}) - 4 x y + (8 y^{2} + 4 y^{2}) + 5 x + (- 3 x - 6 y) + 3$
$= 2 x^{2} - 4 x y + 12 y^{2} + 5 x - 9 y + 3$ is the required answer.

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$6 x^{2} - 4 x y + 5 y^{2} f r o m 8 y^{2} + 6 x y - 3 x^{2}$

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