SOLUTION: Hello Please help me dividing these polynomials (a^3+b^3+c^3-3abc)/(a+b+c)

Question 697108: Hello
Please help me dividing these polynomials
(a^3+b^3+c^3-3abc)/(a+b+c)
Answer by god2012(113) (Show Source): You can put this solution on YOUR website!
Given : (a^3+b^3+c^3-3abc)/(a+b+c)
(a^3+b^3+c^3-3abc) can be written as (a+b+c)(a^2+b^2+c^2-(ab+bc+ac))
Therefore : (a^3+b^3+c^3-3abc)/(a+b+c) = (a^2+b^2+c^2-(ab+bc+ac))
Method 2 : a+b+c )a^3+b^3+c^3-3abc(a^2+b^2+c^2-ab-bc-ac
a^3+a^2b+a^2c subtract
--------------------------
b^3+c^3-a^2b-a^2c-3abc
b^3+ab^2+cb^2 subtract
--------------------------
c^3-a^2b-ab^2-a^2c-cb^2-3abc
c^3+c^2b+c^2a subtract
---------------------------
-a^2b-ab^2-a^2c-cb^2-3abc-c^2b-c^2a
-a^2b-ab^2-abc subtract
---------------------------
-a^2c-cb^2-2abc-c^2b-c^2a
-abc -b^2c-bc^2 subtract
---------------------------
-a^2c-abc+ca^2
- a^2c-abc-ac^2 subtract
---------------------------
0

Quotient = a^2+b^2+c^2-ab-bc-ac

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