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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.

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Multiplying and Dividing Factors

259–266 Multiply or divide, as indicated.

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Simplifying Expressions Using the Order of Operations

267–286 Simplify, applying the order of operations.

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Evaluating Expressions Using the Order of Operations

287–296 Evaluate the expressions.

287. What is 3x² if ?

288. What is if ?

289. What is if ?

290. What is if ?

291. What is if and ?

292. What is if and ?

293. What is if , , and ?

294. What is if ?

295. What is if , , , and ?

296. What is if , , , and ?

Operating with Factorials

297–300 Evaluate the factorial expressions.

297. 3!

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Focusing on Function Notation

301–310 Evaluate the functions for the input value given.

301. If , then

302. If , then

303. If , then

304. If then

305. If , then

306. If , then

307. If , then

308. If , then

309. If , then

310. If , then