What does “collect like terms” mean?
Collecting like terms is a fundamental concept in mathematics, particularly in the field of algebra. It involves grouping together terms that have the same variable(s) raised to the same power. The purpose of collecting like terms is to simplify algebraic expressions and make them easier to work with. In this article, we will explore the definition, importance, and methods of collecting like terms, along with some examples to illustrate the concept.
In algebra, terms are the individual parts of an expression that are separated by addition or subtraction signs. Each term can consist of a coefficient (a numerical value) and a variable (a symbol representing an unknown quantity). For instance, in the expression 3x + 4y – 2x + 6, the terms are 3x, 4y, -2x, and 6.
Importance of collecting like terms
Collecting like terms is crucial for several reasons:
1. Simplification: By grouping like terms, we can reduce the complexity of an expression, making it easier to understand and work with.
2. Preparation for further algebraic operations: Many algebraic operations, such as addition, subtraction, multiplication, and division, require that like terms be collected to simplify the expressions.
3. Solving equations: Collecting like terms is essential when solving equations, as it allows us to isolate the variable on one side of the equation.
Methods of collecting like terms
To collect like terms, follow these steps:
1. Identify the like terms: Look for terms that have the same variable(s) raised to the same power. In the expression 3x + 4y – 2x + 6, the like terms are 3x and -2x, as well as 4y.
2. Combine the coefficients: Add or subtract the coefficients of the like terms. In our example, 3x – 2x equals x, and 4y remains as it is.
3. Write the simplified expression: Combine the simplified like terms to form the new expression. In our example, the simplified expression is x + 4y + 6.
Examples of collecting like terms
Here are some examples to demonstrate the process of collecting like terms:
1. Original expression: 2x + 5x – 3y + 7
Simplified expression: 7x – 3y + 7
2. Original expression: 3a^2 + 2a^2 – 5b + 4b^2
Simplified expression: 5a^2 – 5b + 4b^2
3. Original expression: 4m^3n – 3m^3n + 2mn^2 – mn^2
Simplified expression: m^3n + mn^2
In conclusion, collecting like terms is a vital skill in algebra that simplifies expressions and prepares students for more advanced mathematical concepts. By following the steps outlined in this article, one can effectively collect like terms and make algebraic expressions more manageable.
