Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which expression is equal to (a+b)²?

1. a²+2ab+b²

2. a²-b²

3. (y₂-y₁)/(x₂-x₁)

4. (a-b)(a+b)

The correct answer is: a²+2ab+b²

The expression \((a+b)²\) can be expanded using the distributive property, also known as the FOIL method (First, Outer, Inner, Last). When you calculate \((a+b)(a+b)\), you multiply each term in the first parentheses by each term in the second parentheses. 1. The First terms are \(a \cdot a = a²\). 2. The Outer terms are \(a \cdot b = ab\). 3. The Inner terms are \(b \cdot a = ab\), which is the same as the Outer term. 4. The Last terms are \(b \cdot b = b²\). Adding all these results together gives: \[ a² + ab + ab + b² = a² + 2ab + b². \] This confirms that the expression equivalent to \((a+b)²\) is \(a² + 2ab + b²\). The other options do not represent the expansion of \((a+b)²\). The expression \(a²-b²\) represents the difference of squares and is not related to the expansion of a binomial square. The expression \((y₂-y₁