Write the following in the expanded form:$ (a+2 b+c)^{2} $

Given:

\( (a+2 b+c)^{2} \)

To do:

We have to write the given expression in expanded form.

Solution:

We know that,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

Therefore,

$(a+2 b+c)^{2}=(a)^{2}+(2 b)^{2}+(c)^{2}+2 \times a \times 2 b+2 \times 2 b \times c+2 \times c \times a$

$=a^{2}+4 b^{2}+c^{2}+4 a b+4 b c+2 c a$

Hence, $(a+2 b+c)^{2}=a^{2}+4 b^{2}+c^{2}+4 a b+4 b c+2 c a$.