Answer :

Factors of a2-b2-c2 + 2bc

= a2-(b2 + c2-2bc)


= a2-(b-c)2


=(a + b-c)(a-b + c) … (Using a2-b2=(a + b)(a-b))


Factors of b2-c2-a2 + 2ac


= b2-(c2 + a2-2ac)


=b2-(c-a)2


=(b + c-a)(b-c + a) … (Using a2-b2=(a + b)(a-b))


Factors of c2-a2-b2 + 2ab


= c2-(a2 + b2-2ab)


=c2-(a-b)2


=(c + a-b)(c-a + b) … (Using a2-b2=(a + b)(a-b))


GCD is the greatest common divisor, which is equal to the product of all the common divisors.


the GCD of a2-b2-c2 + 2bc, b2-c2-a2 + 2ac, c2- a2-b2 + 2ab is 1 as no other factor is common to all the three terms


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