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 are equivalent, let's analyze both options: The expressions \( b + 0 \) and \( b \) are equivalent because adding zero to any number does not change its value. This means both expressions represent the same quantity—just as if you have five apples and you add zero more, you still have five apples. On the other hand, \( 4a \) and \( a + 4 \) are not equivalent. The first expression represents four times the value of \( a \), while the second expression adds four to the value of \( a \). For example, if \( a = 2 \), then \( 4a = 8 \) but \( a + 4 = 6\); clearly, they yield different results. In summary, two expressions are considered equivalent if they yield the same value for all possible inputs. This allows us to simplify calculations or express the same idea in different forms!