How do you collect like terms in algebra? This is a fundamental concept in algebra that helps simplify expressions and solve equations. Collecting like terms involves grouping together terms that have the same variables raised to the same powers. By doing so, you can simplify algebraic expressions and make them easier to work with. In this article, we will explore the process of collecting like terms in algebra and provide some examples to illustrate the concept.
Algebraic expressions often contain multiple terms, each consisting of a coefficient and a variable raised to a certain power. For example, in the expression 3x^2 + 2x – 5, the terms are 3x^2, 2x, and -5. To collect like terms, you need to identify terms that have the same variable raised to the same power. In our example, 3x^2 and 2x are like terms because they both have the variable x raised to the second power.
Once you have identified the like terms, you can combine them by adding or subtracting their coefficients. Remember that the variable and its exponent remain the same when combining like terms. Let’s look at an example to illustrate this process:
Example 1:
Consider the expression 5x^2 + 3x^2 – 2x + 4.
To collect like terms, we group the terms with the same variable raised to the same power:
5x^2 + 3x^2 = 8x^2 (combining the coefficients 5 and 3)
-2x remains as it is (no like terms to combine)
Now, we can rewrite the expression with the combined like terms:
8x^2 – 2x + 4
In this example, we have successfully collected the like terms and simplified the expression.
Example 2:
Let’s consider another expression: 4xy + 2xy – 3x – 6y + 5xy.
Grouping the like terms, we have:
4xy + 2xy + 5xy = 11xy (combining the coefficients 4, 2, and 5)
-3x remains as it is (no like terms to combine)
-6y remains as it is (no like terms to combine)
Now, we can rewrite the expression with the combined like terms:
11xy – 3x – 6y
In this example, we have collected the like terms and simplified the expression.
Collecting like terms is an essential skill in algebra that helps simplify expressions and solve equations. By following the process of identifying like terms and combining their coefficients, you can make algebraic expressions more manageable and easier to work with. Remember to always pay attention to the variable and its exponent when combining like terms, as they should remain the same. With practice, you will become more proficient in collecting like terms and applying this concept to a variety of algebraic problems.
