Combining like terms is a fundamental skill in algebra. It involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. For example, $3x^2$ and $-5x^2$ are like terms because they both have $x^2$. We can combine them to get $-2x^2$.
Polynomials are expressions consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Combining like terms in polynomials makes them easier to work with and solve.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Coefficient | A. A term without a variable |
| 2. Variable | B. A symbol representing an unknown value |
| 3. Constant | C. A number multiplied by a variable |
| 4. Like Terms | D. Terms that have the same variable raised to the same power |
| 5. Polynomial | E. An expression with multiple terms, involving variables and coefficients |
Complete the following paragraph with the correct terms:
When combining like terms, you can only add or subtract terms that have the same ______ and ______. The ______ is the number in front of the variable. A ______ is a term that does not have a variable.
Explain in your own words why it is important to combine like terms when working with polynomials. Provide an example.
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