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


Given:

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

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,

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

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

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

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Updated on: 10-Oct-2022

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