=a^2b-a^2c+b^2c-b^2a+c^2a-c^2b
=ab(a-b)+bc(b-c)+ac(c-a)
=b(a^2-ab+cb-c^2)+ac(c-a)
=b[(a+c)(a-c)-b(a-c)]+ac(c-a)
=b(a-c)(a+b-c)-ac(a-c)
=(a-c)(ab+b^2-bc-ac)
=(a-c)(a-b)(b-c)=0
So a-c=0 or a-b=0 or b-c=0.
That is, at least two of the three numbers A, B and C are equal.
Method 2:
To expand the formula, you must
Answer? b-a? c+b? c-b? a+c? b-c? a=0
(a-b)(c? -ab-ac+ab)=0
(a-b)(b-c)(c-a)=0
So: at least two of the three numbers A, B and C are equal.
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