Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which expression represents the difference of squares?

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

2. (a-b)²

3. (a+b)²

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

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

The expression that correctly represents the difference of squares is the product of two binomials: (a-b)(a+b). This expression comes from the identity that states the difference of the squares of two terms can be expressed as the product of the sum and the difference of those two terms. In a general sense, the difference of squares can be described with the formula: a² - b² = (a - b)(a + b). In this case, if we let one term be a and the other term be b, the expression (a-b)(a+b) produces the original difference of squares when expanded. The other expressions do not represent the difference of squares. For instance, (a-b)² and (a+b)² represent perfect squares, which expands to a² - 2ab + b² and a² + 2ab + b², respectively, rather than a simple difference of squares. Similarly, (a+b)(c+d) is an unrelated expression that does not relate to the difference of squares concept. Therefore, the first option is the only choice that accurately fulfills the definition of the difference of squares.