Expand $(2 a + 3 b + 5)^{2}$ using identity

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Solution

$(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2 x y + 2 y z + 2 z x$ ,

On comparing $(x + y + z)^{2}$ with $(2 a + 3 b + 5)^{2}$ ,
$x = 2 a, y = 3 b$ and $z = 5$

Now, by using above identity,
$(2 a + 3 b + 5)^{2} = (2 a)^{2} + (3 b)^{2} + (5)^{2} + 2 (2 a) (3 b) + 2 (3 b) (5) + 2 (5) (2 a)$
$= 4 a^{2} + 9 b^{2} + 25 + 12 a b + 30 b + 20 a$

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