Final answer:
The correct answer is option a. The product of (a - b)(a - b) is a² - 2ab + b², not a² - b², so the expression equals a² - b² never. Expansion of the expression using the FOIL method demonstrates this.
Step-by-step explanation:
The student has asked whether the product of (a − b)(a − b) is a² − b². To address this question, let's expand the expression using the FOIL method (First, Outside, Inside, Last), which is used for multiplying two binomials.
Expanding (a − b)(a − b) we get:
- First: a * a = a²
- Outside: a * (−b) = −ab
- Inside: (−b) * a = −ab
- Last: (−b) * (−b) = b²
When we combine these terms, the expression simplifies to a² − 2ab + b².
Therefore, the statement that the product (a − b)(a − b) is equal to a² − b² is incorrect. Instead, the correct product is a² − 2ab + b². The only time (a − b)(a − b) would equal a² − b² is if ab were equal to zero, which is not generally the case. Thus, the correct option is a. never.