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What is the product of [tex]\((a-5)\)[/tex] and [tex]\((a+3)\)[/tex]?

A. [tex]\(-15\)[/tex]
B. [tex]\(a^2 + 2a - 15\)[/tex]
C. [tex]\(a^2 - 2a - 15\)[/tex]

Sagot :

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].