Question

Chứng minh \({\left( {a - b} \right)^3} =  - {\left( {b - a} \right)^3}\) 

Answer 1

\(\begin{array}{l}{\left( {a - b} \right)^3} = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\\ - {\left( {b - a} \right)^3} =  - \left( {{b^3} - 3{b^2}a + 3b{a^2} - {a^3}} \right) = {a^3} - 3{a^2}b + 3a{b^2} - {b^3}\end{array}\)

Vậy \({\left( {a - b} \right)^3} =  - {\left( {b - a} \right)^3}\) (đpcm).