prove that (a+b+c) cube - a cube - b cube - c cube = 3(a+b)(b+c)(c+a)
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(a+b+c)3 - a3-b3-c3=LHS
LHS=(a+b+c)2 ×(a+b+c)- (a-b)(a2+ab+b2)-c3
=(a2 +b2+c2+2ab+2bc+2ca)(a+b+c) -(a-b)(a2+ab+b2)-c3
=a3+ab2+ac2+2a2b+2abc+2ca2+a2b+b3.....
Rest you can do
LHS=(a+b+c)2 ×(a+b+c)- (a-b)(a2+ab+b2)-c3
=(a2 +b2+c2+2ab+2bc+2ca)(a+b+c) -(a-b)(a2+ab+b2)-c3
=a3+ab2+ac2+2a2b+2abc+2ca2+a2b+b3.....
Rest you can do
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