( a %2B b %2B c ) ^ 3 - a ^ 3 - b ^ 3 - c ^ 3 = 3 ( a

1.	( a %2B b %2B c ) ^ 3 - a ^ 3 - b ^ 3 - c ^ 3 = 3 ( a %2B b ) ( b %2B c ) ( c %2B a )
Answer» (a+b+c)3 - a3-b3-c3 = [(a+b)+c]3 – a3-b3-c3 (a+b)3+c3+3c(a+b)(a+b+c)-a3-b3-c3 A3+b3+3ab(a+b)+c3+3c(a+b)(a+b+c)-a3-b3-c3 A3+b3+c3+3ab(a+b)+3c(a+b)(a+b+c)-a3-b3-c3 3ab(a+b)+3c(a+b)(a+b+c) 3(a+b)[ab+c(a+b+c)] 3(a+b)[ab+ac+bc+c2] 3(a+b)[a(b+c)+c(b+c)] 3(a+b)(b+c)(c+a)

( a %2B b %2B c ) ^ 3 - a ^ 3 - b ^ 3 - c ^ 3 = 3 ( a %2B b ) ( b %2B c ) ( c %2B a )

Answer»

(a+b+c)3 - a3-b3-c3 = [(a+b)+c]3 – a3-b3-c3

(a+b)3+c3+3c(a+b)(a+b+c)-a3-b3-c3

A3+b3+3ab(a+b)+c3+3c(a+b)(a+b+c)-a3-b3-c3

A3+b3+c3+3ab(a+b)+3c(a+b)(a+b+c)-a3-b3-c3

3ab(a+b)+3c(a+b)(a+b+c) 3(a+b)[ab+c(a+b+c)]

3(a+b)[ab+ac+bc+c2] 3(a+b)[a(b+c)+c(b+c)]

3(a+b)(b+c)(c+a)