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