Chapter 6—Expressions and Equations
6-3 Combining Like Terms
When you complete the work for this section, you should be able to: - Demonstrate how to combine numerical values in an algebraic expression or equation.
- Demonstrate how to combine literal terms in an algebraic expression or equation.
- Explain how literal terms can be combined only when they have the same factors raised to the same power
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Definition Like terms are terms that have the same factors raised to the same power. |
Combining Numerical Values
Procedure Combining like terms: Numerical Values - When the numerical values are all on the same side of the equal sign:
Perform the indicated operations |
Example
Problem Simplify this equation by combining like terms: y = 4 + 5 | |
| Procedure | |
Add the numerical terms on the right side of the equal sign. | Y = 4 + 5
Y = 9 |
| Solution | |
Combining like terms for y = 4 + 5, we get y = 9 | |
Combining Literal Terms
Literal terms are the terms in an expression or equation that are represented by letters. They are the variable terms (as opposed to the numerical terms).
Procedure Combining like terms: Literal Terms Important: Only the same literal terms can be combined. - When literal terms are on the same side of the equal sign: Combine the like terms by performing the indicated operations
- When literal terms are on opposite sides of the equal sign:
- Rewrite the equation so that all the literal terms are on one side of the equal sign (typically the left side).
- Combine the like terms by performing the indicated operations
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Example
Problem Simplify this equation by combining like terms: x + y = 2 – y | |
| Procedure | |
- Gather the literal terms on the left side of the equal sign.
| x + y = 2 – y
x + y + y = 2 |
- Perform the indicated operations
| x + 2y = 2 |
| Solution | |
Combining like terms for x + y = 2 – y, we get x + 2y = 2 | |
Literal terms can be combined only when they have the same power. For example, 2x2 and x2 can be combined because both terms are raised to the same power — power of 2. But 2x2 cannot be combined with x. Why not? Because one of the x terms is raised to the power of 2 and the other is not.
- So 2x2 + x2 can be combined as 3x2
- But 2x2 + x cannot be combined, and must remain expressed as 2x2 + 2x.
Example
Problem Simplify this equation by combining like terms:
4x2 + 3x + 2 = x2 – x + 3 | |
| Procedure | |
Gather the literal terms on the left side of the equal sign. | 4x2 + 3x + 2 = x2 – x + 3
4x2 – x2 + 3x + x = 3 – 2 |
Combine the x2 terms | 4x2 – x2 + 3x + x = 3 – 2
3x2 + 3x + x = 3 – 2 |
Combine the x terms | 3x2 + 3x + x = 3 – 2
3x2 + 4x = 3 – 2 |
Combine the numerical terms | 3x2 + 4x = 3 – 2
3x2 + 4x = 1 |
| Solution | |
Simplifying by combining like terms, 4x2 + 3x + 2 = x2 – x + 3 becomes 3x2 + 4x = 1 | |
