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1. $x^{2} + 4 y^{2} + 8 x - 16 y + 16$

Answer: Option C

Explanation:

{(a + b + C)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a x^{2} + 4 y^{2} + 8 x - 16 y + 16 = x^{2} + 16 + 4 y^{2} + 8 x - 16 y = {(x)}^{2} + {(4)}^{2} + {(- 2 y)}^{2} + 2 . x . 4 + 2 . (- 2 y) . 4 + 2 . (- 2 y) . x = {(x + 4 - 2 y)}^{2}

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