How to Simplify by Collecting Like Terms
Simplifying algebraic expressions is a fundamental skill in mathematics that helps students understand the properties of numbers and the relationships between different variables. One of the most common techniques used to simplify algebraic expressions is by collecting like terms. In this article, we will discuss how to simplify by collecting like terms and provide some examples to illustrate the process.
Understanding Like Terms
Before we dive into the process of collecting like terms, it’s important to understand what like terms are. Like terms are terms that have the same variable(s) raised to the same power. For example, in the expression 3x^2 + 2x^2, the terms 3x^2 and 2x^2 are like terms because they both have the variable x raised to the second power.
Collecting Like Terms
To simplify an algebraic expression by collecting like terms, follow these steps:
1. Identify the like terms in the expression.
2. Add or subtract the coefficients of the like terms.
3. Write the simplified expression with the combined like terms.
Let’s look at some examples to illustrate this process.
Example 1
Simplify the expression: 5x + 3x + 2x – 4
Step 1: Identify the like terms. In this case, the like terms are 5x, 3x, and 2x.
Step 2: Add or subtract the coefficients of the like terms. 5 + 3 + 2 = 10, and -4 remains the same.
Step 3: Write the simplified expression with the combined like terms. The simplified expression is 10x – 4.
Example 2
Simplify the expression: 4a^2 + 2a^2 – 3a^2 + 5a^2
Step 1: Identify the like terms. The like terms in this expression are 4a^2, 2a^2, -3a^2, and 5a^2.
Step 2: Add or subtract the coefficients of the like terms. 4 + 2 – 3 + 5 = 8.
Step 3: Write the simplified expression with the combined like terms. The simplified expression is 8a^2.
Example 3
Simplify the expression: 7xy + 3xy – 2xy + 4x^2y
Step 1: Identify the like terms. The like terms in this expression are 7xy, 3xy, and -2xy.
Step 2: Add or subtract the coefficients of the like terms. 7 + 3 – 2 = 8.
Step 3: Write the simplified expression with the combined like terms. The simplified expression is 8xy + 4x^2y.
Conclusion
Collecting like terms is a valuable technique for simplifying algebraic expressions. By following the steps outlined in this article, students can master this skill and become more proficient in their algebraic problem-solving abilities. Remember, practice makes perfect, so keep working on simplifying expressions with like terms to improve your skills.
