Evaluate [a+b+c]^3 - a^3-b^3-c^3.

[a+b+c]^3 – a^3-b^3-c^3.

=a^3 +b^3 +c^3 + 3ab(a + b) + 3bc(b +c) + 3ac(a +c) + 6abc – a^3-b^3-c^3

= 3ab(a + b) + 3bc(b +c) + 3ac(a +c) + 6abc

= 3(ab(a + b) + bc(b +c) + ac(a +c) + 2abc)

= 3(ab(a + b) + b^2c + abc + bc^2 + ac^2 + a^2c + abc)

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

= 3(a + b)(c^2 + bc + ab +. ac)

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

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

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