Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the expanded form of a(b+c)?

1. ab+ac

2. ac+ad+bc+bd

3. (a+b)(c+d)

4. (y₂-y₁)/(x₂-x₁)

The correct answer is: ab+ac

The expanded form of the expression a(b+c) involves applying the distributive property, which states that when you multiply a term by a sum, you must multiply the term by each addend in the sum. In this case, multiplying a by (b+c) means that you distribute a to both b and c. Therefore, you get: - First, a multiplied by b, which gives you ab. - Then, a multiplied by c, resulting in ac. When you combine these two products, you arrive at the expression ab + ac. This clearly embodies the distributive property in action and is the correct expanded form of a(b+c). Other options do not reflect this process or represent the same expression. The second option includes terms that arise from a different kind of distribution, while the third option suggests a factored expression rather than an expanded one. The fourth option is unrelated to multiplication or expansion in the context of this problem. Thus, ab + ac is the accurate and straightforward expanded form of the given expression.