Subtract $5 x^{2} - 7 x y - 2 y^{2}$ from $3 x^{2} + 5 x y + 2 y^{2}$ using horizontal method.

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Solution

Given that: Subtract $5 x^{2} - 7 x y - 2 y^{2}$ from $3 x^{2} + 5 x y + 2 y^{2}$ .
Subtracting $5 x^{2} - 7 x y - 2 y^{2}$ from $3 x^{2} + 5 x y + 2 y^{2}$ using the horizontal method:
$= 3 x^{2} + 5 x y + 2 y^{2}$ $- (5 x^{2} - 7 x y - 2 y^{2})$
$= 3 x^{2} + 5 x y + 2 y^{2}$ $- 5 x^{2} + 7 x y + 2 y^{2}$
$= 3 x^{2} - 5 x^{2} + 2 y^{2} + 2 y^{2} + 5 x y + 7 x y$
$= - 2 x^{2} + 4 y^{2} + 12 x y = 2 (- x^{2} + 2 y^{2} + 6 x y)$
Hence, the given expression will be $2 (- x^{2} + 2 y^{2} + 6 x)$

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