Factors of ac, ab, bc, and a2

To solve this problem, we need to find the factors of the given expressions. Factors are the numbers that can be multiplied to get the original expression. Let's take each expression one by one.

ac = a * c
ab = a * b
bc = b * c
a2 = a * a

Factors of ac: a, c, ac, 1
Factors of ab: a, b, ab, 1
Factors of bc: b, c, bc, 1
Factors of a2: a, a, a2, 1

Common factors: a, 1

Out of the given options, the only one that has the common factors is option B.

Option B: (a + c)(a + b) = a2 + ab + ac + bc

This expression has all the common factors: a, 1. Therefore, option B is the correct answer.

Explanation:

The factors of an expression are the numbers that can be multiplied to get the original expression. In this problem, we have four expressions: ac, ab, bc, and a2. We need to find the factors of these expressions.

To find the factors of these expressions, we need to break them down into their prime factors. For example, ac can be written as a * c. Similarly, ab can be written as a * b, bc can be written as b * c, and a2 can be written as a * a.

Once we have the prime factors, we can find all the possible factors by multiplying the prime factors in different combinations. For example, the factors of ac can be a * c, a, c, 1. Similarly, the factors of ab can be a * b, a, b, 1. The same applies to bc and a2.

After finding the factors of each expression, we need to look for the common factors. In this problem, the common factors are a and 1.

Out of the given options, only option B has all the common factors. Therefore, option B is the correct answer.