Let's simplify this expression step by step:
(а+1)(а-3) - (а-2)(а+1)= а^2 - 3а + а - 3 - (а^2 + 2а - а - 2)= а^2 - 3а + а - 3 - а^2 - 2а + а + 2= а^2 - а - 1
So, the simplified expression is а^2 - а - 1.
Let's simplify this expression step by step:
(а+1)(а-3) - (а-2)(а+1)
= а^2 - 3а + а - 3 - (а^2 + 2а - а - 2)
= а^2 - 3а + а - 3 - а^2 - 2а + а + 2
= а^2 - а - 1
So, the simplified expression is а^2 - а - 1.