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Chapter 1: Problem 85

Explain how to add like terms. Give an example.

Short Answer

Expert verified
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 by step solution

01

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.
02

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 \(8x - y\)
03

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.

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