If $A = 25 x^{2} + 64 y^{2}$ then the term to be added to $A$ to make it a perfect square is:

80 x y

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- 40 x y

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40 x y

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160 x y

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Solution

The correct option is A $80 x y$
$A = 25 x^{2} + 64 y^{2}$
To make this perfect, we have to add a term $A x y .$
Using ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
$\Rightarrow$ add $2 (5 x) (8 y) = 80 x y$
So, $25 x^{2} + 64 y^{2} + 80 x y = {(5 x + 8 y)}^{2}$ is perfect square.
Therefore, $80 x y$ has to be added.
Hence, the answer is $80 x y .$

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