Expand: $ (m+2 n+3 \gamma)^{2} $

Given: $ (m+2 n+3 r)^{2} $

To do: Expand the expression given

Solution:

We will use the identity
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

$ (m+2 n+3r)^{2} $

$(m)^2+(2n)^2+(3r)^2+2.m.2n+2.2n.3r+2.3r.m$

$m^2+4n^2+9 r^2+4mn+12nr+6rm$

Therefore the expansion of  $ (m+2 n+3 r)^{2} $ is $m^2+4n^2+9 r^2+4mn+12nr+6rm$