Expand $(x + 2 y)^{2}$

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Solution

$(x + 2 y)^{2} = x^{2} + 2 (x) (2 y) + (2 y)^{2}$
$= x^{2} + 4 x y + 4 y^{2}$
Aliter: $(x + 2 y)^{2} = (x + 2 y) (x + 2 y)$
$= x (x + 2 y) + 2 y (x + 2 y)$
$= x^{2} + 2 x y + 2 y x + 4 y^{2} [∵ x y = y z]$
$= x^{2} + 4 x y + 4 y^{2}$

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