The expression that is not a perfect square is

4 x^{2} + 28 x y + 49 y^{2}

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25 x^{2} - 40 x y - 16 y^{2}

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x^{2} - 6 x y + 9 y^{2}

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

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Solution

The correct option is B $25 x^{2} - 40 x y - 16 y^{2}$
$4 x^{2} + 28 x y + 49 y^{2} = 2 (2 x) (7 y) + (7 y)^{2} = (2 x + 7 y)^{2}$
$x^{2} - 6 x y + 9 y = x^{2} - 2 (x) (3 y) + (3 y)^{2} = (x - 3 y)^{2}$
$a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a = (a + b + c)^{2}$
But $25 x^{2} - 40 x y - 16 y^{2} \neq (5 a)^{2} - 2 (5 x) (4 y) + (4 y)^{2}$

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