Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

How can a² - 2ab + b² be expressed?

1. (a-b)²

2. (a-b)(a+b)

3. (a+b)(a+b)

4. -b±[√b²-4ac]/2a

The correct answer is: (a-b)²

The expression a² - 2ab + b² represents a perfect square trinomial. A perfect square trinomial can be factored into the square of a binomial, specifically in the form (x - y)² = x² - 2xy + y². In this case, if we let x = a and y = b, we can see that a² is the square of a, b² is the square of b, and -2ab represents twice the product of a and b (with a negative sign). Therefore, a² - 2ab + b² can be factored as (a - b)², which confirms why this is the correct expression. The other options do not represent the correct factoring of the original expression. The binomial product expressions (a-b)(a+b) and (a+b)(a+b) do not relate to the structure of a² - 2ab + b². The formula involving the square root is for solving quadratic equations, which is not applicable in this context.