Which Expression Is Equivalent To The Expression Below?
In mathematics, two expressions are considered equivalent if they have the same value for all possible values of the variables in the expressions. In other words, if you plug in the same value for each variable in both expressions, you will get the same answer.
To find the equivalent expression for a given expression, you can use a variety of techniques, including:
- Combining like terms: Combine terms that have the same variable and coefficient.
- Factoring: Factor out common factors from the expression.
- Expanding: Expand parentheses or other algebraic operations.
- Simplifying: Combine like terms, factor out common factors, and cancel common factors.
Here are some examples of how to find equivalent expressions:
Example 1:
Original expression: 2x + 3 + 4x - 1 Combining like terms: (2x + 4x) + (3 - 1) Simplifying: 6x + 2 Example 2:
Original expression: (x - 2)(x + 3) Factoring: x(x + 3) - 2(x + 3) Expanding: x^2 + 3x - 2x - 6 Combining like terms: x^2 + x - 6 Example 3:
Original expression: 2(x + 1)(x - 1) Factoring out a 2: 2(x + 1)(x - 1) Simplifying: 2(x^2 - 1) Questions Related to Which Expression Is Equivalent To The Expression Below
Here are some questions that you can ask to help you find the equivalent expression for a given expression:
- Can I combine any like terms?
- Can I factor the expression?
- Can I expand the expression?
- Can I simplify the expression by combining like terms, factoring out common factors, and canceling common factors?
Here are some examples of how to answer these questions:
Example 1:
Original expression: 2x + 3 + 4x - 1 Can I combine any like terms?
Answer: Yes, I can combine the terms 2x and 4x.
New expression: (2x + 4x) + (3 - 1) Can I factor the expression?
Answer: No, the expression is already in its simplest form.
Example 2:
Original expression: (x - 2)(x + 3) Can I combine any like terms?
Answer: No, there are no like terms.
Can I factor the expression?
Answer: Yes, I can factor the expression as follows:
New expression: x(x + 3) - 2(x + 3) Can I expand the expression?
Answer: Yes, I can expand the expression as follows:
New expression: x^2 + 3x - 2x - 6 Can I simplify the expression by combining like terms, factoring out common factors, and canceling common factors?
Answer: Yes, I can combine the terms x^2 and -2x.
New expression: x^2 + x - 6 Conclusion
Finding the equivalent expression for a given expression is a common task in mathematics. By using the techniques described above, you can find the equivalent expression for any given expression.