Problem 85 - Introductory Algebra for College Students

Question

Explain how to add like terms. Give an example.

Step-by-Step Solution

Answer

Adding like terms involves adding the coefficients of the terms with the same variable and power. For example, in the expression \(3x + 2y + 5x - 3y\), the like terms are added as follows: \(3x + 5x = 8x\) and \(2y - 3y = -y\), so the simplified expression is \(8x - y\).

Step 1: Identify the Like Terms

Let's begin with an algebraic expression, for example \(3x + 2y + 5x - 3y\). Like terms here will be \(3x\) and \(5x\), as well as \(2y\) and \(-3y\), since they have the same variables.

Step 2: Add the Like Terms

Next, add the coefficients of these like terms together. For \(3x\) and \(5x\), add the coefficients 3 and 5 together to get 8. For \(2y\) and \(-3y\), add the coefficients 2 and -3 together to get -1. The new expression then becomes \(8x - y\)

Step 3: Write the Final Expression

Finally include the variable part after the addition of the coefficients which gives the simplified expression. Here, \(8x - y\) will be the final simplified expression after adding like terms.