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Addition and Subtraction of Algebraic Expression

Find the sum ...

Question

Find the sum of $x^{2} - {2 y}^{2}, {2 x}^{2} - 4 x y + {5 y}^{2}, {6 y}^{2} + 11 x y - {6 x}^{2}$

A

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

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B

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

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C

9 y^{2} + 7 x y - 3 x^{2}

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D

2 x^{2} - 7 x y + y^{2}

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Solution

The correct option is C $9 y^{2} + 7 x y - 3 x^{2}$
Required sum $= {(x}^{2} - {2 y}^{2}) + {(2 x}^{2} - 4 x y + {5 y}^{2}) + {(6 y}^{2} + 11 x y - {6 x}^{2})$
$= (x^{2} + {2 x}^{2} - {6 x}^{2}) + ({- 2 y}^{2} + {5 y}^{2} + {6 y}^{2}) + (- 4 x y + 11 x y)$ (Combining like terms)
$= - 3 x^{2} + {9 y}^{2} + 7 x y$ .

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Similar questions

(4 x^{2} - 7 x y + 4 y^{2} - 3), (5 + 6 y^{2} - 8 x y + x^{2})

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

Q. Form an equation

a x^{2} + b x y + c y^{2}

by subtracting the sum of

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

y^{2} - 2 x y - 3 x^{2}

from the sum of

6 x^{2} - 8 x y - y^{2}

2 x y - 2 y^{2} - x^{2}

a + b + c

Q. Subtract the sum of

x^{3} + x^{2} - 7 x y + 2 y^{2} + 56 x

- 6 x^{3} + 9 x^{2} - 24 x y - 79 x

from the sum of

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

7 x^{2} - 16 x y + 6 y^{2} + 6 x

.

Q. The transformed equation of

3 x^{2} + 3 y^{2} + 2 x y = 2

when the coordinate axes are rotated through an angle

45^{\circ}

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

2 y^{2} + 6 x^{2} y^{2} - x y

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