Simplify the following:
$(2 x + 5 y)^{2} + (2 x - 5 y)^{2}$

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Solution

$(2 x + 5 y)^{2} + (2 x - 5 y)^{2}$ $[U s i n g, (a \pm b)^{2} = a^{2} \pm 2 a b + b^{2}]$
$= (2 x)^{2} + 2 \times 2 x \times 5 y + (5 y)^{2} + (2 x)^{2} - 2 \times 2 x \times 5 y + (5 y)^{2}$
$= 4 x^{2} + 20 x y + 25 y^{2} + 4 x^{2} - 20 x y + 25 y^{2}$
$= 8 x^{2} + 50 y^{2}$

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