Problem 80 - Introductory and Intermediate Algebra for College Students 4th

Question

What are like terms? Provide an example with your description.

Step-by-Step Solution

Answer

Like terms refer to the terms in an equation that have the same variables and powers. The coefficients don't need to be the same. An example is \(8y\) and \(2y\), which are like terms because they both contain \(y\) raised to the power of 1.

Step 1: Defining Like Terms

Like terms in algebra are terms that have the exact same variables and each corresponding variable has the same exponent. Terms are separated by addition or subtraction operators.

Step 2: Identifying Coefficients

The coefficient of a term is the numerical or constant part of the term. The coefficients do not have to match for the terms to be considered alike. For instance, in the term \(4x\), \(4\) is the coefficient.

Step 3: Providing Examples

An example of like terms could be \(3x^2\) and \(7x^2\). Both terms have the same variable, \(x\), and the same exponent, \(2\). The coefficients (3 and 7), however, are different. So, even though the coefficients are different, they are considered like terms because they share the same variable raised to the same power.