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Algebraic Identities

Simplify the ...

Question

Simplify the following expression: $(2 l - m + 6 n)^{2}$

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Solution

We know that $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
Here, $a = 2 l, b = - m, c = 6 n$
$(2 l - m + 6 n)^{2} = (2 l)^{2} + (- m)^{2} + (6 n)^{2} + 2.2 l . (- m) + 2. (- m) .6 n + 2.6 n .2 l$
$=$ $4 l^{2} + m^{2} + 36 n^{2} - 4 l m - 12 m n + 24 l n$
Therefore, $(2 l - m + 6 n)^{2} = 4 l^{2} + m^{2} + 36 n^{2} - 4 l m - 12 m n + 24 l n$

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