Докажите, что: (a+1)^3-(a+1)=a(a+1)(a+2).

\[(a + 1)^{3} - (a + 1) =\]

\[= a(a + 1)(a + 2)\]

\[(a + 1)\left( (a + 1)^{2} - 1 \right) =\]

\[= a(a + 1)(a + 2)\]

\[(a + 1)(a + 1 - 1)(a + 1 + 1) =\]

\[= a(a + 1)(a + 2)\]

\[(a + 1) \cdot a \cdot (a + 2) =\]

\[= a(a + 1)(a + 2)\]

\[a(a + 1)(a + 2) = a(a + 1)(a + 2)\]

\[Что\ и\ требовалось\ доказать.\]