докажите что если ab+bc+ac=0 то (a-b)(a-c)+(b-c)(b-a)+(c-a)(c-b)+a^2+b^2+c^2

-a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 (a-b)(b-c)(c-a)

Reformatting the input :

Changes мейд to your input should not affect the solution:

 (1): "c2"   was replaced by   "c^2".  2 more similar replacement(s).

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Step  1  : c2 Simplify c - a Equation at the end of step  1  : (a2) (b2) c2 (((a-c))+((b-a)))+((c-b)) (a-b) (b-c) c-a Step  2  :Equation at the end of step  2  : (a2) (b2) c2(c-b) (((a-c))+((b-a)))+ (a-b) (b-c) c-a Step  3  : b2 Simplify b - c Equation at the end of step  3  : (a2) b2 c2(c-b) (((a-c))+((b-a)))+ (a-b) b-c c-a Step  4  :Equation at the end of step  4  : (a2) b2(b-a) c2(c-b) (((a-c))+)+ (a-b) b-c c-a Step  5  : a2 Simplify a - b Equation at the end of step  5  : a2 b2(b-a) c2(c-b) (((a-c))+)+ a-b b-c c-a Step  6  :Equation at the end of step  6  : a2(a-c) b2(b-a) c2(c-b) (+)+ a-b b-c c-a Step  7  :Calculating the Least Common Multiple :

 7.1    Find the Least Common Multiple 

      The left denominator is :       a-b 

      The right denominator is :       b-c 

                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic    
    Factor     Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 Left,Right  a-b 101 b-c 011

      Least Common Multiple: 
      (a-b)  (b-c) 

Calculating Multipliers :

 7.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = b-c

   Right_M = L.C.M / R_Deno = a-b

Making Equivalent Fractions :

 7.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well. 

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. L. Num. a2 (a-c) (b-c) = L.C.M (a-b) (b-c) R. Mult. R. Num. b2 (b-a) (a-b) = L.C.M (a-b) (b-c) Adding fractions that have a common denominator :

 7.4       Adding up the two equivalent fractions 
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a2 (a-c) (b-c) + b2 (b-a) (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 = (a-b) (b-c) (a - b) (b - c) Equation at the end of step  7  : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 (c - b) + (a - b) (b - c) c - a Step  8  :Calculating the Least Common Multiple :

 8.1    Find the Least Common Multiple 

      The left denominator is :       (a-b)  (b-c) 

      The right denominator is :       c-a 

                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic    
    Factor     Left 
 Denominator  Right 
 Denominator  L.C.M = Max 
 Left,Right  a-b 101 b-c 101 c-a 011

      Least Common Multiple: 
      (a-b)  (b-c)  (c-a) 

Calculating Multipliers :

 8.2    Calculate multipliers for the two fractions 


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = c-a

   Right_M = L.C.M / R_Deno = (a-b)(b-c)

Making Equivalent Fractions :

 8.3      Rewrite the two fractions into equivalent fractions

L. Mult. L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) (c-a) = L.C.M (a-b) (b-c) (c-a) R. Mult. R. Num. c2 (c-b) (a-b) (b-c) = L.C.M (a-b) (b-c) (c-a) Adding fractions that have a common denominator :

 8.4       Adding up the two equivalent fractions 

(a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) (c-a) + c2 (c-b) (a-b) (b-c) -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 = (a-b) (b-c) (c-a) (a-b) (b-c) (c-a) Final result : -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 (a-b)(b-c)(c-a)

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Latest drills solved(-4,7)to(94,-55)(5)/(7)+(4)/(y)=38(x+8/9)-9a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b)