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:

What to Watch Out For

Here are a few more things to keep in mind:

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 + 4 − 7ab + 6b − ab − 4

258. x + 3 − y + 4 − z² + 5 − 2

Multiplying and Dividing Factors

259–266 Multiply or divide, as indicated.

259. 4(3x)

260. −9(5y)

261.

262.

263. 3xy(4xy²)

264. −5yz²(3y²z)

265.

266.

Simplifying Expressions Using the Order of Operations

267–286 Simplify, applying the order of operations.

267. 2 + 6 · 3

268. 9 − 8 ÷ 4

269. 3 · 2 + 4(−3)

270. −6 ÷ 3 − 4 ÷ 2

271.

272.

273. 6 − 4 · 2 + 8 ÷ 4 − 1

274. 20 ÷ 5 + 4 · 3 − 1

275. 10 − 4 − 8 + 6 · 2

276. 36 ÷ 6 ÷ 3 + 3 · 2 · 5

277. 4(6 − 3)

278. 5(−3 + 2)

279.

280.

281.

282.

283. 3 + 2(6−4)

284. 8 − 7(1 + 3)

285. 4(6 + 1)−8(3 + 2)

286.

Evaluating Expressions Using the Order of Operations

287–296 Evaluate the expressions.

287. What is 3x² if x = −2?

288. What is −5x − 1 if x = −3?

289. What is x(2 - x) if x = 4?

290. What is if x = −2?

291. What is 2(l + w) if l = 4 and w = 3?

292. What is bh if b = 9 and h = 4?

293. What is a₀+(n−1)d if a₀ = 4, n = 11, and d = 3?

294. What is C + 32 if C = 40?

295. What is A if A = 100, r = 2, n = 1, and t = 3?

296. What is if x = 6, a = 4, b = 3, and c = 5?

Operating with Factorials

297–300 Evaluate the factorial expressions.

297. 3!

298. 6! − 3!

299.

300.

Focusing on Function Notation

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

301. If f(x) = x² + 3x + 1, then f(2) =

302. If g(x) = 9 − 3x², then g(−1) =

303. If h(x) = , then h(−4) =

304. If k(x) = , then k(10) =

305. If n(x) = x³ + 2x², then n(2) =

306. If p(x) = , then p(3) =

307. If q(x) = x! + (x−1)!, then q(4) =

308. If r(x) = , then r(8) =

309. If t(x) = , then t(−3) =

310. If w(x) = , then w(4) =