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