Tính \({\left( {a - b - c} \right)^3}\).

Ta có: \({\left( {a - b - c} \right)^3}\)

\[ = {\left[ {\left( {a - b} \right) - c} \right]^3}\]

\( = {\left( {a - b} \right)^3} - 3{\left( {a - b} \right)^2}c + 3\left( {a - b} \right){c^2} - {c^3}\)

\( = {a^3} - 3{a^2}b + 3a{b^2} - {b^3} - 3c\left( {{a^2} - 2ab + {b^2}} \right) + 3a{c^2} - 3b{c^2} - {c^3}\)

\( = {a^3} - {b^3} - {c^3} - 3ab\left( {a - b} \right) - 3ac\left( {a - c} \right) - 3bc\left( {b + c} \right) + 6abc\).