Write $(2 x + 3 y + 5 z)^{2}$ in an expanded from

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Solution

$(2 x + 3 y + 5 z)^{2}$
Using, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$= (2 x)^{2} + (3 y)^{2} + (5 z)^{2} + 2 (2 x) (3 y) + 2 (3 y) (5 z) + 2 (5 z) (2 x)$
$= 4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x .$

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