Chapter 6

Creating More User-Friendly Algebraic Expressions

Algebraic expressions involve terms (separated by addition and subtraction) and factors (connected by multiplication and division). Part of the challenge of working with algebraic expressions is in using the correct rules: the order of operations, rules of exponents, distributing, and so on. Function notation helps simplify some expressions by providing a rule and inviting evaluation.

The Problems You'll Work On

In this chapter, you get to put some of those algebraic rules to practice with the following types of problems:

  • Finding the sums and differences of like terms
  • Multiplying and dividing terms and performing the operations logically
  • Applying the order of operations when simplifying expressions
  • Evaluating algebraic expressions when variables are assigned specific values
  • Using the factorial operation
  • Getting acquainted with function notation

What to Watch Out For

Here are a few more things to keep in mind:

  • Recognizing like terms and the processes involved when combining them
  • Reducing fractions correctly — dividing by factors of all the terms
  • Evaluating expressions within grouping symbols before applying the order of operations
  • Reducing fractions involving factorials correctly

Adding and Subtracting Like Terms

251–258 Simplify by combining like terms.

251. 4a + 6a

252. 9xy + 4xy − 5xy

253. 5z − 3 − 2z + 7

254. 6y + 4 − 3 − 8y

255. 7a + 2b + ab − 3 + 4a − 2b − 5ab

256. 3x2 + 2x − 1 + 4x2 − 5x + 3

257. 9 − 3z

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