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$(2 x - 7 y)^{2} + 28 x y = 4 x^{2} + 49 y^{2}$

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Solution

L.H.S
$(2 x - 7 y)^{2} + 28 x y$
$= 4 x^{2} + 49 y^{2} - 2 \times 2 \times 7 x y + 28 x y$ $[∵ (a - b)^{2} = a^{2} + b^{2} - 2 a b]$
$= 4 x^{2} + 49 y^{2} - 28 x y + 28 x y$
$= 4 x^{2} + 49 y^{2}$
$= R . H . S$
Hence proved.

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