Short Answer 
To determine if two mathematical expressions are equivalent, first simplify each expression by eliminating terms and grouping like terms. Next, substitute specific values for variables in both expressions and compare the results to check for equivalence. Finally, analyze whether the simplified forms and evaluated results are the same to confirm if the expressions are equivalent.
Step 1: Simplify the Expressions
To determine if two mathematical expressions are equivalent, the first step is to simplify each expression. This involves a few strategies:
- Eliminate terms where possible to reduce complexity.
- Group like terms together to make calculations easier.
- Apply mathematical operations such as addition, subtraction, multiplication, and division appropriately.
Step 2: Substitute Variable Values
If simplification isn’t yielding a clear answer, the next step is to substitute actual values for any variables in the expressions. By doing this, you can evaluate each expression at specific points, which can help clarify whether they yield the same result:
- Choose specific values for each variable in both expressions.
- Calculate the results of each expression using those values.
- Compare the resulting values to see if they are the same.
Step 3: Analyze Results for Equivalence
The final step involves analyzing the results obtained from the previous steps. By comparing the simplified forms and the evaluated results, you can determine if the expressions are equivalent:
- If both expressions simplify to the same result, they are equivalent.
- If both evaluated expressions yield the same numerical value, this also indicates equivalence.
- In case of discrepancies, revisit the simplification and substitution steps to ensure accuracy.