Problem 85 - Introductory and Intermediate Algebra for College Students 4th

Question

Explain how to add like terms. Give an example.

Step-by-Step Solution

Answer

To add like terms, identify terms with the same variables and the same powers, then add the coefficients of these terms. For example, in the expression 2x + 5y + 3x + 7y, it simplifies to 5x + 12y.

Step 1: Understand the Concept of Like Terms

Like terms are defined as terms that contain the same variables with same powers. The numbers accompanying the variables can be different and are known as the coefficients. For example, 3x and 4x are like terms because they contain the same variable 'x' with same power 1, but different coefficients 3 and 4.

Step 2: Identify Like Terms in the Expression

Consider an expression such as 2x + 5y + 3x + 7y. In this expression, 2x and 3x are like terms, as they both contain the same variable x with power 1. Similarly, 5y and 7y are like terms, as they both contain the variable y with power 1.

Step 3: Add the Coefficients of Like Terms

We add like terms by adding their coefficients while keeping the variable and the power the same. The 2x and 3x becomes \(2x + 3x = 5x\). Similarly, adding 5y and 7y becomes \(5y + 7y = 12y\).

Step 4: Write the Final Answer

The final expression after adding all like terms becomes 5x + 12y, which can't be simplified further as 5x and 12y are not like terms, they have different variables.