(a+b)^3 +(b+c)^3 +(c+a)^3 -3(a+b) (b+c) (c+a)=2(a^3+b^3+c^3-3abc)

1.	(a+b)^3 +(b+c)^3 +(c+a)^3 -3(a+b) (b+c) (c+a)=2(a^3+b^3+c^3-3abc)
Answer» Let a + b =x, b + c =y and c + a = z. Then,(a + b)3 + (b + c)3 + (c + a)3 - 3(a + b)(b + c) (c + a)= x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)= {(a + b) + (b + c) + (c + a)} {(a + b)2 + (b + c)2 + (c + a)2- (a + b)(b + c) - (b + c)(c + a) - (c + a) (a + b)}= 2(a + b + c) {a2 + b2 + 2ab + b2 + c2 + 2bc + c2 + 2ca + a2\xa0- (ab + ac + b2 + bc) - (bc + ba + c2 + ca) - (ca + cb + a2 + ab)}= 2(a + b + c) (a2 + b2 + c2 - ab - bc - ca) = 2(a3 + b3 + c3 - 3abc)

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