a2b2+b2c2+4c2a2+2ab2c-4a2bc-4abc2=?
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Solution :
a²b²+b²c²+4c²a²+2ab²c-4a²bc-4abc²
= (ab)²+(bc)²+(-2ca)²+2*ab*bc+2*bc*(-2ca)
+ 2*(-2ca)*(ab)
= ( ab + bc - 2ca )²
= ( ab + bc - 2ca )( ab + bc - 2ca )
••••
a²b²+b²c²+4c²a²+2ab²c-4a²bc-4abc²
= (ab)²+(bc)²+(-2ca)²+2*ab*bc+2*bc*(-2ca)
+ 2*(-2ca)*(ab)
= ( ab + bc - 2ca )²
= ( ab + bc - 2ca )( ab + bc - 2ca )
••••
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