Simplify :
(3x + 2y - 9) (2x - 6y + 2) - [(4x - 9y - 1) + (-3x + 8y + 7)]

6 x^{2} - 14 x y - 12 y^{2} - 13 x + 59 y - 24

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6 x^{2} - 12 x y - 189 - 17 x + 61 y - 29

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8 x^{2} - 14 x y - 12 y^{2} - 13 x + 57 y - 24

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8 x^{2} - 14 x y - 12 y^{2} - 17 x + 61 y - 29

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Solution

The correct option is D $6 x^{2} - 14 x y - 12 y^{2} - 13 x + 59 y - 24$
Given expression is $(3 x + 2 y - 9) (2 x - 6 y + 2) - [(4 x - 9 y - 1) + (- 3 x + 8 y + 7)]$
We can perform the given operations to simplify the expression further.
$= (6 x^{2} - 18 x y + 6 x + 4 x y + 4 y - 12 y^{2} - 18 x + 54 y - 18) - [4 x - 9 y - 1 - 3 x + 8 y + 7]$
$\Rightarrow 6 x^{2} - 12 y^{2} - 14 x y - 12 x + 58 y - 18 - x + y - 6$
$\Rightarrow 6 x^{2} - 12 y^{2} - 14 x y - 13 x + 59 y - 24$

Hence, $(3 x + 2 y - 9) (2 x - 6 y + 2) - [(4 x - 9 y - 1) + (- 3 x + 8 y + 7)] = 6 x^{2} - 12 y^{2} - 14 x y - 13 x + 59 y - 24$

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Similar questions

Equation of a line which is parallel to the line common to the pair of lines given by $6 x^{2} - x y - 12 y^{2} - 0$ and $15 x^{2} + 14 x y - 8 y^{2} - 0$ and at a distance 7 from it is

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Simplify :(3x + 2y - 9) (2x - 6y + 2) - [(4x - 9y - 1) + (-3x + 8y + 7)]

Simplify :
(3x + 2y - 9) (2x - 6y + 2) - [(4x - 9y - 1) + (-3x + 8y + 7)]