2.3: Evaluate, Simplify, and Translate Expressions (Part 1)
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- Evaluate algebraic expressions
- Identify terms, coefficients, and like terms
- Simplify expressions by combining like terms
- Translate word phrases to algebraic expressions
Before you get started, take this readiness quiz.
- Is
- Simplify
. If you missed this problem, review Example 2.1.6. - Simplify
Evaluate Algebraic Expressions
In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
Evaluate
Solution
- To evaluate, substitute
for in the expression, and then simplify.
| Substitute. | |
| Add. |
When
- To evaluate, substitute
for in the expression, and then simplify.
| Substitute. | |
| Add. |
When
Evaluate:
- Answer a
-
- Answer b
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Evaluate:
- Answer a
-
- Answer b
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Evaluate
Solution
Remember
- To evaluate the expression when
for , and then simplify.
| Substitute |
|
| Multiply. | |
| Subtract. |
- To evaluate the expression when
for , and then simplify.
| Substitute |
|
| Multiply. | |
| Subtract. |
Notice that in part (a) that we wrote
Evaluate:
- Answer a
-
- Answer b
-
Evaluate:
- Answer a
-
- Answer b
-
Evaluate
Solution
We substitute
| Substitute |
|
| Use the definition of exponent. | |
| Multiply |
When
Evaluate:
- Answer
-
Evaluate:
- Answer
-
Evaluate
Solution
In this expression, the variable is an exponent.
| Substitute |
|
| Use the definition of exponent. | |
| Multiply |
When
Evaluate:
- Answer
-
Evaluate:
- Answer
-
Evaluate
Solution
This expression contains two variables, so we must make two substitutions.
| Substitute |
|
| Multiply. | |
| Add and subtract left to right. |
When
Evaluate:
- Answer
-
Evaluate:
- Answer
-
Evaluate
Solution
We need to be careful when an expression has a variable with an exponent. In this expression,
| Substitute |
|
| Simplify 42. | |
| Multiply. | |
| Add. |
Evaluate:
- Answer
-
Evaluate:
- Answer
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Identify Terms, Coefficients, and Like Terms
Algebraic expressions are made up of terms. A term is a constant or the product of a constant and one or more variables. Some examples of terms are
The constant that multiplies the variable(s) in a term is called the coefficient. We can think of the coefficient as the number in front of the variable. The coefficient of the term
| Term | Coefficient |
|---|---|
| 7 | 7 |
| 9a | 9 |
| y | 1 |
| 5x2 | 5 |
An algebraic expression may consist of one or more terms added or subtracted. In this chapter, we will only work with terms that are added together. Table
| Expression | Terms |
|---|---|
| 7 | 7 |
| y | y |
| x + 7 | x, 7 |
| 2x + 7y + 4 | 2x, 7y, 4 |
| 3x2 + 4x2 + 5y + 3 | 3x2, 4x2, 5y, 3 |
Identify each term in the expression
Solution
The expression has four terms. They are
The coefficient of
The coefficient of
Remember that if no number is written before a variable, the coefficient is
The coefficient of a constant is the constant, so the coefficient of
Identify all terms in the given expression, and their coefficients:
- Answer
-
The terms are
and . The coefficients are and .
Identify all terms in the given expression, and their coefficients:
- Answer
-
The terms are
and , The coefficients are and .
Some terms share common traits. Look at the following terms. Which ones seem to have traits in common?
Which of these terms are like terms?
- The terms
and are both constant terms. - The terms
and are both terms with . - The terms
and both have .
Terms are called like terms if they have the same variables and exponents. All constant terms are also like terms. So among the terms
Terms that are either constants or have the same variables with the same exponents are like terms.
Identify the like terms:
Solution
Look at the variables and exponents. The expression contains
Look at the variables and exponents. The expression contains the terms
Identify the like terms in the list or the expression:
- Answer
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; and , , and
Identify the like terms in the list or the expression:
- Answer
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and ; and ; and
Simplify Expressions by Combining Like Terms
We can simplify an expression by combining the like terms. What do you think
We can see why this works by writing both terms as addition problems.
Add the coefficients and keep the same variable. It doesn’t matter what
The expression
Now it is easier to see the like terms to be combined.
Step 1. Identify like terms.
Step 2. Rearrange the expression so like terms are together.
Step 3. Add the coefficients of the like terms.
Simplify the expression:
Solution
| Identify the like terms | |
| Rearrange the expression, so the like terms are together. | |
| Add the coefficients of the like terms. | |
| The original expression is simplified to... |
Simplify:
- Answer
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Simplify:
- Answer
-
Simplify the expression:
Solution
| Identify the like terms. | |
| Rearrange the expression so like terms are together. | |
| Add the coefficients of the like terms. |
These are not like terms and cannot be combined. So
Simplify:
- Answer
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Simplify:
- Answer
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Contributors and Attributions
- Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a Creative Commons Attribution License 4.0 license.
