What should be added to the product of $(x^{2} + x y - y^{2})$ and $(x^{2} - x y + y^{2})$ to get $x^{2} y^{2}$ ?

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

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

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

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

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Solution

The correct option is A $2 x^{2} y^{2} - x^{4} - 2 x y^{3} + y^{4}$
$(x^{2} + x y - y^{2}) (x^{2} - x y + y^{2}) = x^{2} (x^{2} - x y + y^{2}) + x y (x^{2} - x y + y^{2}) - y^{2} (x^{2} - x y + y^{2})$
$= x^{4} + 2 x y^{3} - x^{2} y^{2} - y^{4}$
Let the algebraic expression to be added be $A$ . Then
$A = x^{2} y^{2} - (x^{4} + 2 x y^{3} - x^{2} y^{2} - y^{4})$
$= x^{2} y^{2} - x^{4} - 2 x y^{3} + x^{2} y^{2} + y^{4}$
$= 2 x^{2} y^{2} - x^{4} - 2 x y^{3} + y^{4}$

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Similar questions

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

x^{4} - y^{4}

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

(x^{2} - y^{2}) : (x^{2} + y^{2})

(x^{4} - y^{4}) : (x + y)^{4}

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

x^{4} + x^{2} y^{2} + y^{4} = 133

\frac{x^{4} - y^{4}}{x^{2} + y^{2}}

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