To find the product of [tex]\((a - 5)\)[/tex] and [tex]\((a + 3)\)[/tex], we can use the distributive property, also known as the FOIL (First, Outer, Inner, Last) method.
1. First: Multiply the first terms from each binomial:
[tex]\[ a \cdot a = a^2 \][/tex]
2. Outer: Multiply the outer terms from each binomial:
[tex]\[ a \cdot 3 = 3a \][/tex]
3. Inner: Multiply the inner terms from each binomial:
[tex]\[ -5 \cdot a = -5a \][/tex]
4. Last: Multiply the last terms from each binomial:
[tex]\[ -5 \cdot 3 = -15 \][/tex]
Next, we combine all these products:
[tex]\[ a^2 + 3a - 5a - 15 \][/tex]
Now, we simplify by combining the like terms:
[tex]\[ a^2 + (3a - 5a) - 15 \][/tex]
[tex]\[ a^2 - 2a - 15 \][/tex]
Therefore, the product of [tex]\((a - 5)\)[/tex] and [tex]\((a + 3)\)[/tex] is:
[tex]\[ \boxed{A^2 - 2a - 15} \][/tex]
Thus, the correct answer is C. [tex]\( A^2 - 2a - 15 \)[/tex].
