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

Given:

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

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,

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

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

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

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Updated on: 10-Oct-2022

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