Fast And correct With steps...U'll be the BRAINLIEST..

1.	Fast And correct With steps...U'll be the BRAINLIEST..
Answer» Answer: 2(a+b+c) + a(a-b) + b(b-a) + c(c-b) Step-by-step explanation: In this question, we are gonna use the identity of a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca). (a+b)^3 + (b+c)^3 + (c+a)^3 -3(a+b)(b+c)(c+a) = (a+b+b+c+a+c)(a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-(ab+ac+b^2+bc)-(ba+bc+ca+c^2)-(a^2+ac+ba+bc)) Now, after simplifying, (2a+2b+2c)(a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-ab-ac-b^2-bc-ba-bc-ca-c^2-a^2-ac-ba-bc) Now, after CANCELLING the terms and simplifying, (2a+2b+2c)(a^2+b^2+c^2-ba-ca-bc) After further simplification, 2(a+b+c)+a(a-b) +b(b-a) + c(c-b) {FINAL ANSWER} PLEASE mark me as brainliest..

Answer»

Answer:

2(a+b+c) + a(a-b) + b(b-a) + c(c-b)

Step-by-step explanation:

In this question, we are gonna use the identity of a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

(a+b)^3 + (b+c)^3 + (c+a)^3 -3(a+b)(b+c)(c+a) = (a+b+b+c+a+c)(a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-(ab+ac+b^2+bc)-(ba+bc+ca+c^2)-(a^2+ac+ba+bc))

Now, after simplifying,

(2a+2b+2c)(a^2+b^2+2ab+b^2+c^2+2bc+c^2+a^2+2ac-ab-ac-b^2-bc-ba-bc-ca-c^2-a^2-ac-ba-bc)

Now, after CANCELLING the terms and simplifying,

(2a+2b+2c)(a^2+b^2+c^2-ba-ca-bc)

After further simplification,

2(a+b+c)+a(a-b) +b(b-a) + c(c-b) {FINAL ANSWER}

PLEASE mark me as brainliest..

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