Expand $(2 x + 3 y)^{2}$

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Solution

$(2 x + 3 y)^{2} = (2 x)^{2} + 2 (2 x) (3 y) + (3 y)^{2}$
$= 4 x^{2} + 12 x y + 9 y^{2}$
Aliter: $(2 x + 3 y)^{2} = (2 x + 3 y) (2 x + 3 y)$
$= 2 x (2 x + 3 y) + 3 y (2 x + 3 y)$
$= (2 x) (2 x) + (2 x) (3 y) + (3 y) (2 x) + (3 y) (3 y)$
$= 4 x^{2} + 6 x y + 6 y x + 9 y^{2} [∵ x y = y x]$
$(2 x + 3 y)^{2} = 4 x^{2} + 12 x y + 9 y^{2}$

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