The problem asks us to expand and simplify the expression $(a + 2)(a - 3) - 3(a - 5)$.

1. Problem Description

The problem asks us to expand and simplify the expression $(a + 2)(a - 3) - 3(a - 5)$.

2. Solution Steps

First, we expand the product of the two binomials:

$(a + 2)(a - 3) = a(a) + a(-3) + 2(a) + 2(-3) = a^2 - 3a + 2a - 6 = a^2 - a - 6$

Next, we distribute the $-3$ to the expression in the second parentheses:

$-3(a - 5) = -3a + 15$

Now, we combine the expanded expressions:

$(a + 2)(a - 3) - 3(a - 5) = (a^2 - a - 6) + (-3a + 15) = a^2 - a - 6 - 3a + 15$

Finally, we combine like terms:

$a^2 - a - 3a - 6 + 15 = a^2 - 4a + 9$

3. Final Answer

The simplified expression is $a^2 - 4a + 9$.