How to Collect Like Terms in Mathematics
Collecting like terms in mathematics is a fundamental skill that is essential for solving algebraic equations and simplifying expressions. Like terms are terms that contain the same variable raised to the same power. By collecting like terms, we can simplify complex expressions and make them easier to work with. In this article, we will discuss the steps and techniques for collecting like terms in mathematics.
Understanding Like Terms
Before we dive into the process of collecting like terms, it is important to understand what they are. Like terms are terms that have the same variable raised to the same power. For example, in the expression 3x^2 + 5x^2 + 2x, the terms 3x^2 and 5x^2 are like terms because they both have the variable x raised to the second power. Similarly, the term 2x is not a like term because it has the variable x raised to the first power.
Identifying Like Terms
To collect like terms, the first step is to identify them. Look for terms that have the same variable raised to the same power. In the example above, we can see that 3x^2 and 5x^2 are like terms. Once you have identified the like terms, you can proceed to the next step.
Combining Like Terms
Once you have identified the like terms, the next step is to combine them. To do this, add or subtract the coefficients of the like terms while keeping the variable and its exponent the same. In our example, we can combine 3x^2 and 5x^2 as follows:
3x^2 + 5x^2 = (3 + 5)x^2 = 8x^2
This means that the original expression, 3x^2 + 5x^2 + 2x, can be simplified to 8x^2 + 2x.
Practical Examples
Let’s look at a few practical examples to illustrate the process of collecting like terms:
1. Combine the like terms in the expression 4x^3 + 2x^3 – 3x^3 + 5x^3.
– 4x^3 + 2x^3 – 3x^3 + 5x^3 = (4 + 2 – 3 + 5)x^3 = 8x^3
2. Simplify the expression 7a^2 + 3a^2 – 2a^2 – 4a^2.
– 7a^2 + 3a^2 – 2a^2 – 4a^2 = (7 + 3 – 2 – 4)a^2 = 4a^2
3. Combine the like terms in the expression 3xy + 2xy – 5xy + 4xy.
– 3xy + 2xy – 5xy + 4xy = (3 + 2 – 5 + 4)xy = 4xy
Conclusion
Collecting like terms in mathematics is a crucial skill that can help simplify complex expressions and make algebraic equations easier to solve. By following the steps outlined in this article, you can master the process of identifying and combining like terms. With practice, you will be able to simplify expressions and solve equations with confidence.
