Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the result of factoring a² + 2ab + b²?

1. (a+b)²

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

3. (y₂-y₁)/(x₂-x₁)

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

The correct answer is: (a+b)²

The expression a² + 2ab + b² can be recognized as a perfect square trinomial. This type of trinomial is a result of squaring a binomial. Specifically, the general form of a perfect square trinomial can be expressed as (x + y)² = x² + 2xy + y². In your case, if we identify x as "a" and y as "b", substituting these into the formula gives us: (a + b)² = a² + 2ab + b². Thus, the correct result of factoring a² + 2ab + b² is indeed (a + b)². This perfect square trinomial encapsulates the fundamental property that when a binomial is squared, the result is the sum of the squares of the individual terms plus twice their product. This recognition is crucial in algebra as it simplifies quadratic expressions effectively. The other options do not apply to the given expression. For instance, (a - b)(a + b) represents the difference of squares, which does not correlate with the original expression. Additionally, the expressions involving coordinates (y₂ - y₁)/(x₂ - x₁) and (a + b)(