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IMAS 2013–2014 Junior Division — Round 2 Question 2

IMAS · IMAS 2013–2014 Junior Division — Round 2

Question 2

What is the value of the expression $(a-b)(a+b-c)+(b-c)(b+c-a)+(c-a)(c+a-b)$?
  1. $0$
  2. $a^2+b^2+c^2$
  3. $ab+bc+ca$
  4. $a^2+b^2+c^2-ab-bc-ca$
  5. $a^2+b^2+c^2+ab+bc+ca$