Circle the pair of equivalent expressions. Then explain what it means for two expressions to be equivalent. \[ b+0 \text { and } b \] \( 4 a \) and \( a+4 \)

To determine which pair of expressions is equivalent, we need to analyze each pair: 1. **First Pair: \( b + 0 \) and \( b \)** - The expression \( b + 0 \) simplifies to \( b \) because adding zero to any number does not change its value. Therefore, these two expressions are equivalent. 2. **Second Pair: \( 4a \) and \( a + 4 \)** - The expression \( 4a \) represents four times the value of \( a \), while \( a + 4 \) represents the value of \( a \) increased by four. These two expressions are not equivalent because they yield different results for any value of \( a \). ### Conclusion: The equivalent expressions are \( b + 0 \) and \( b \). ### Explanation of Equivalent Expressions: Two expressions are considered equivalent if they have the same value for all possible values of their variables. In other words, no matter what numbers you substitute for the variables in the expressions, they will always yield the same result. In this case, \( b + 0 \) and \( b \) are equivalent because they produce the same output regardless of the value of \( b \).