Write the Following in Expanded Form
\[ (a^2 + b^2 + c^2)^2 \]
Solution:
Using identity:
\[ (x+y+z)^2 = x^2+y^2+z^2+2xy+2yz+2zx \]
\[ (a^2 + b^2 + c^2)^2 \]
\[ = (a^2)^2 + (b^2)^2 + (c^2)^2 + 2(a^2)(b^2) + 2(b^2)(c^2) + 2(c^2)(a^2) \]
\[ = a^4 + b^4 + c^4 + 2a^2b^2 + 2b^2c^2 + 2c^2a^2 \]