Question

The product of (a − b)(a − b) is a² − b².

a. Sometimes

b. Always

c. Never

Answer 1

The product of (a - b)(a - b) is always equal to a² - 2ab + b², not a² - b². Therefore, the correct answer to the question is 'c. Never'.

Step-by-step explanation:

The student's question asks whether the product of (a − b)(a − b) equals a² − b² sometimes, always, or never. To address this question, we need to perform the multiplication of the binomials. The product (a − b)(a − b), also known as the square of a binomial, is found by applying the FOIL method (First, Outside, Inside, Last). Multiplying the terms, we get:

• First: a²

• Outside: -ab

• Inside: -ab

• Last: +b²

When we combine like terms, the equation simplifies to:

a² - 2ab + b²

This result is distinctly different from a² − b², which is the difference of squares and is obtained when multiplying (a + b)(a − b). Therefore, the statement that the product of (a − b)(a − b) equals a² − b² is incorrect. So, the mention correct option in the final part is c. Never.