Expand (a+3)(a−5).

Expand (a+3)(a−5).

• A. a^2 -2a +15
• B. a^2 -8a -15
• C. a^2 -2a -15
• D. a^2 +2a -15

Answer: (C)

Expanding binomials uses distributing each term in one binomial to every term in the other, then combining like terms. Multiply a by a to get a^2. Then a times -5 gives -5a, and 3 times a gives +3a. Finally, 3 times -5 gives -15. Combine the a-terms: -5a + 3a = -2a. Put it all together: a^2 - 2a - 15. The middle term is negative because the cross terms subtract, and the constant is negative because 3 and -5 multiply to -15. This is the correct expanded form; the other forms would have the wrong sign on the middle term or the constant.

Expanding binomials uses distributing each term in one binomial to every term in the other, then combining like terms. Multiply a by a to get a^2. Then a times -5 gives -5a, and 3 times a gives +3a. Finally, 3 times -5 gives -15. Combine the a-terms: -5a + 3a = -2a. Put it all together: a^2 - 2a - 15. The middle term is negative because the cross terms subtract, and the constant is negative because 3 and -5 multiply to -15. This is the correct expanded form; the other forms would have the wrong sign on the middle term or the constant.