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Addition and Subtraction of Algebraic Expression

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Question

ExampleAdd $(2 x^{2} + 6 y + 3 x y), (3 x^{2} - 5 x y - x)$ and $(6 x y + 5)$ .

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Solution

$(2 x^{2} + 6 y + 3 x y) + (3 x^{2} - 5 x y - x) + (6 x y + 5)$
$(2 x^{2} + 3 x^{2}) + (3 x y - 5 x y + 6 x y) + 6 y - x + 5$
$5 x^{2} + 4 x y - x + 6 y + 5$

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(x) (2 x + 3 y - 4 z)

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Q. State True or False:

The sides of a triangle is

x^{2} - 3 x y + 8

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

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Q. From the sum of x² + 3y² − 6xy, 2x² − y² + 8xy, y² + 8 and x² − 3xy subtract −3x² + 4y² − xy + x − y + 3.

Q. Find the equation to the common conjugate diameters of the conics (1)

x^{2} + 4 x y + 6 y^{2} = 1

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2 x^{2} - 5 x y + 3 y^{2} = 1

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