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Math: Basic Tutorials : Addition and Subtraction of Polynomials
Addition and Subtraction of Polynomials
In an algebraic expression, we can identify like terms as terms that have the same variables raised to the same exponents. This section will show you how to add and subtract polynomials by combining like terms.
Examples
Click on the titles below to view each example.
Example 1. Find the sum of open parenthesis 4x squared minus 5x plus 1 close parenthesis plus open parenthesis 3x squared minus 8x minus 9 close parenthesis.
Line 1: Identify the like terms in the expression. Like terms have the same variable and the same exponent so in this expression 4x squared and 3x squared are like terms, negative 5x and negative 8x are like terms, and 1 and negative 9 are like terms.
Line 2: Rearrange the expression to get the like terms together so the expression is 4x squared plus 3x squared minus 5x minus 8x plus 1 minus 9.
Line 3: Combine the like terms to simplify the expression to 7x squared minus 13x minus 8.
Example 2. Find the difference of open parenthesis 9m squared minus 7m plus 4 close parenthesis minus open parenthesis m squared minus 3m plus 8 close parenthesis.
Line 1: First, multiply each term in the second set of parentheses by negative 1 to remove the parentheses. This will change the signs of the terms in the second set of parentheses, so the expression is 9m squared minus 7m plus 4 minus m squared plus 3m minus 8.
Line 2: Identify the like terms in the expression. Like terms have the same variable and the same exponent, so in this expression 9m squared and negative m squared are like terms, negative 7m and 3m are like terms, and 4 and negative 8 are like terms.
Line 3: Rearrange the expression to get the like terms together so the expression is 9m squared minus m squared minus 7m plus 3m plus 4 minus 8.
Line 4: Combine the like terms to simplify the expression to 8m squared minus 4m minus 4.
Summary and Worksheet
- Summary: Adding and Subtracting Polynomials - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Adding and Subtracting Polynomials - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.
Attribution
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window