(a+3)(5-a)-(a-1)²

To simplify the expression \((a+3)(5-a)-(a-1)²\), we will first expand both parts and then combine like terms.

1. Expand \((a+3)(5-a)\): \[ (a+3)(5-a) = a \cdot 5 + a \cdot (-a) + 3 \cdot 5 + 3 \cdot (-a) = 5a - a^2 + 15 - 3a \] Combining like terms, we have: \[ 5a - 3a - a^2 + 15 = 2a - a^2 + 15 \]

2. Expand \((a-1)²\): \[ (a-1)² = a² - 2a + 1 \]

3. Combine both expansions: Now substitute both expansions back into the original expression: \[ (2a - a^2 + 15) - (a² - 2a + 1) \] Distributing the negative sign: \[ 2a - a^2 + 15 - a^2 + 2a - 1 \]

4. Combine like terms: \[ -a^2 - a^2 + 2a + 2a + 15 - 1 = -2a^2 + 4a + 14 \]

Thus, the simplified expression is: \[ -2a^2 + 4a + 14 \]