Final answer:
To simplify the product (a-3)(a-2), the distributive property is used to multiply each term in the first parenthesis by each term in the second, resulting in the simplified form a^2 - 5a + 6.
Step-by-step explanation:
The product of (a-3)(a-2) can be simplified using the distributive property. The distributive property states that a(b + c) = ab + ac. Applying this property to the product at hand, we first multiply each term in the first parenthesis by each term in the second parenthesis:
a * a + a * (-2) + (-3) * a + (-3) * (-2).
Combining like terms, this results in:
a2 - 2a - 3a + 6,
Which simplifies to:
a2 - 5a + 6.
The final expression a2 - 5a + 6 is the simplified form of the product (a-3)(a-2).