Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which identity corresponds to a² - b²?

1. (a-b)(a+b)

2. (a+b)²

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

4. (a-b)²

The correct answer is: (a-b)(a+b)

The expression a² - b² is recognized as the difference of squares. This algebraic identity states that the difference between the squares of two numbers can be factored into the product of the sum and the difference of those two numbers. In this case, a² - b² can be factored to (a - b)(a + b). This makes intuitive sense because when you multiply (a - b) by (a + b) using the distributive property (also known as FOIL for binomials), you will yield: 1. The first terms: a * a = a² 2. The outer terms: a * b = ab 3. The inner terms: -b * a = -ab 4. The last terms: -b * b = -b² When combining the outer and inner terms, the +ab and -ab cancel each other out, leaving you with a² - b² as a result. Thus, the identity for a² - b² correctly corresponds to (a - b)(a + b), verifying that the choice selected is valid. The other options do not represent the difference of squares. For instance, (a + b)² would expand to a