Rút gọn các biểu thức: (a+b+c)^3 -(b+c-a)^3 -(a+c-b)^3

* Hướng dẫn giải

$$\begin{gathered} {\left(a+b+c\right)}^3-{\left(b+c-a\right)}^3-{\left(a+c-b\right)}^3-{\left(a+b-c\right)}^3 \\ \begin{array}{l}={\left[a+\left(b+c\right)\right]}^3-{\left[\left(b+c\right)-a\right]}^3-{\left[a-\left(b-c\right)\right]}^3-{\left[a-\left(b-c\right)\right]}^3\\ =6{\left(b+c\right)}^{2}a+2a^3-2a^3-6a{\left(b-c\right)}^2\\ =24abc\end{array} \end{gathered}$$