30 points!!?????answer this with explanation
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Use identity a3 + b3 + c3 = (a + b + c)(a2 + b2 + c2- ab - bc- ca) + 3abc
If a + b + c = 0; then, a3 + b3 + c3= 3abc
Here, (a2-b2) + (b2-c2) + (c2-a2)
= 0
So, (a2-b2)3 + (b2-c2)3 + (c2-a2)3
= 3 * (a2-b2) * (b2-c2) * (c2-a2)
= 3 * (a + b)(a - b) * (b+ c)(b-c) * (c + a)(c - a)
= 3 (a + b)(b+ c)(c + a)(a - b)(b-c)(c - a) (Proved)
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