(а-2)(а-1)-а(а+1)

To simplify the expression \( (a-2)(a-1) - a(a+1) \), we will first expand both parts of the expression and then combine like terms.

1. Expand \( (a-2)(a-1) \): \[ (a-2)(a-1) = a^2 - a - 2a + 2 = a^2 - 3a + 2 \]

2. Expand \( a(a+1) \): \[ a(a+1) = a^2 + a \]

3. Now, substitute these expansions back into the original expression: \[ (a^2 - 3a + 2) - (a^2 + a) \]

4. Distribute the negative sign: \[ a^2 - 3a + 2 - a^2 - a \]

5. Combine like terms: \[ (a^2 - a^2) + (-3a - a) + 2 = 0 - 4a + 2 = -4a + 2 \]

Thus, the simplified expression is: \[ -4a + 2 \]