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All Textbook Solutions for Elementary Algebra
In the following exercises, add or subtract the polynomials. 64. (m2+2n2)+(m28mnn2)In the following exercises, add or subtract the polynomials. 65. (u2v2)(u24uv3v2)In the following exercises, add or subtract the polynomials. 66. (j2k2)(j28jk5k2)In the following exercises, add or subtract the polynomials. 67. (p33p2q)+(2pq2+4q3)(3p2q+pq2)In the following exercises, add or subtract the polynomials. 68. (a32a2b)+(ab2+b3)(3a2b+4ab2)In the following exercises, add or subtract the polynomials. 69. (x3x2y)(4xy2y3)+(3x2yxy2)In the following exercises, add or subtract the polynomials. 70. (x32x2y)(xy23y3)(x2y4xy2)In the following exercises, evaluate each polynomial for the given value. 71. Evaluate 8y23y+2 when: (a) y=5 (b) y=2 (c) y=0In the following exercises, evaluate each polynomial for the given value. 72. Evaluate 5y2y7 when: (a) y=4 (b) y=1 (c) y=0In the following exercises, evaluate each polynomial for the given value. 73. Evaluate 436x when: (a) x=3 (b) x=0 (c) x=1In the following exercises, evaluate each polynomial for the given value. 74. Evaluate 1636x2 when: (a) x=1 (b) x=0 (c) x=2In the following exercises, evaluate each polynomial for the given value. 75. A painter drops a brush from a platform 75 feet high. The polynomial 16t2+75 gives the height of the brush t seconds after it was dropped. Find the height after t=2 seconds.In the following exercises, evaluate each polynomial for the given value. 76. A girl drops a ball off a cliff into the ocean. The polynomial 16t2+250 gives the height of a ball t seconds after it is dropped from a 250-foot tall cliff. Find the height after t=2 seconds.In the following exercises, evaluate each polynomial for the given value. 77. A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial 4p2+420p . Find the revenue received when p=60 dollars.In the following exercises, evaluate each polynomial for the given value. 78. A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial 4p2+420p . Find the revenue received when p=90 dollars.Fuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial 1150x2+13x . Find the fuel efficiency when x=30 mph.Stopping Distance The number of feet it takes for a car traveling at x miles per hour to stop on dry, level concrete is given by the polynomial 0.06x2+1.1x . Find the stopping distance when x=40 mph .Rental Cost The cost to rent a rug cleaner for d days is given by the polynomial 5.50d+25 . Find the cost to rent the cleaner for 6 days.Height of Projectile The height (in feet) of an object projected upward is given by the polynomial 16t2+60t+90 where t represents time in seconds. Find the height after t=2.5 seconds.Temperature Conversion The temperature in degrees Fahrenheit is given by the polynomial 95c+32 where c represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when c=65 .Using your own words, explain the difference between a monomial, a binomial, and a trinomial.Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.Ariana thinks the sum 6y2+5y4 is 11y6 . What is wrong with her reasoning?Jonathan thinks that 13 and 1x are both monomials. What is wrong with his reasoning?Simplify: (a) 63 (b) 151 (c) (37)2 (d) (0.43)2Simplify: (a) 25 (b) 211 (c) (25)3 (d) (0.218)2 .Simplify: (a) (3)4 (b) 34 .Simplify: (a) (13)2 (b) 132 .Simplify: b9b8 .Simplify: x12x4 .Simplify: (a) 553 (b) 4949 .Simplify: (a) 7678 (b) 101010Simplify: (a) p5p (b) y14y29 .Simplify: (a) zz7 (b) b15b34.Simplify: x6x4x8 .Simplify: b5b9b5Simplify: (a) (b7)5 (b) (54)3 .Simplify: (a) (z6)9 (b) (37)7Simplify: (a) (12y)2 (b) (2wx)5 .Simplify: (a) (5wx)3 (b) (3y)3 .Simplify: (a) (a4)5(a7)4 (b) (2c4d2)3 .Simplify: (a) (3x6y7)4 (b) (q4)5(q3)3 .Simplify: (a) (5n)2(3n10) (b) (c4d2)5(3cd5)4 .Simplify: (a) (a3b2)6(4ab3)4 (b) (2x)3(5x7) .Multiply: (5y7)(7y4) .Multiply: (6b4)(9b5) .Multiply: (25a4b3)(15ab3) .Multiply: (23r5s)(12r6s7) .In the following exercises, simplify each expression with exponents. 88. (a) 35 (b) 91 (c) (13)2 (d) (0.2)4In the following exercises, simplify each expression with exponents. 89. (a) 104 (b) 171 (c) (29)2 (d) (0.5)3In the following exercises, simplify each expression with exponents. 90. (a) 26 (b) 141 (c) (25)3 (d) (0.7)2In the following exercises, simplify each expression with exponents. 91. (a) 83 (b) 81 (c) (34)3 (d) (0.4)3In the following exercises, simplify each expression with exponents. 92. (a) (6)4 (b) 64In the following exercises, simplify each expression with exponents. 93. (a) (2)6 (b) 26In the following exercises, simplify each expression with exponents. 94. (a) (14)4 (b) (14)4In the following exercises, simplify each expression with exponents. 95. (a) (23)2 (b) (23)2In the following exercises, simplify each expression with exponents. 96. (a) 0.52 (b) (0.5)2In the following exercises, simplify each expression with exponents. 97. (a) 0.14 (b) (0.1)4In the following exercises, simplify each expression using the Product Property for Exponents. 98. d3d6In the following exercises, simplify each expression using the Product Property for Exponents. 99. x4x2In the following exercises, simplify each expression using the Product Property for Exponents. 100. n19n12In the following exercises, simplify each expression using the Product Property for Exponents. 101. q27q15In the following exercises, simplify each expression using the Product Property for Exponents. 102. (a) 4549 (b) 898In the following exercises, simplify each expression using the Product Property for Exponents. 103. (a) 31036 (b) 554In the following exercises, simplify each expression using the Product Property for Exponents. 104. (a) yy3 (b) z25z8In the following exercises, simplify each expression using the Product Property for Exponents. 105. (a) w5w (b) u41u53In the following exercises, simplify each expression using the Product Property for Exponents. 106. ww2w3In the following exercises, simplify each expression using the Product Property for Exponents. 107. yy3y5In the following exercises, simplify each expression using the Product Property for Exponents. 108. a4a3a9In the following exercises, simplify each expression using the Product Property for Exponents. 109. c5c11c2In the following exercises, simplify each expression using the Product Property for Exponents. 110. mxm3In the following exercises, simplify each expression using the Product Property for Exponents. 111. nyn2In the following exercises, simplify each expression using the Product Property for Exponents. 112. yaybIn the following exercises, simplify each expression using the Product Property for Exponents. 113. xpxqIn the following exercises, simplify each expression using the Product Property for Exponents. 114. (a) (m4)2 (b) (103)6In the following exercises, simplify each expression using the Product Property for Exponents. 115. (a) (b2)7 (b) (38)2In the following exercises, simplify each expression using the Product Property for Exponents. 116. (a) (y3)x (b) (5x)yIn the following exercises, simplify each expression using the Product Property for Exponents. 117. (a) (x2)y (b) (7a)bIn the following exercises, simplify each expression using the Product Property for Exponents. 118. (a) (6a)2 (b) (3xy)2In the following exercises, simplify each expression using the Product Property for Exponents. 119. (a) (5x)2 (b) (4ab)2In the following exercises, simplify each expression using the Product Property for Exponents. 120. (a) (4m)3 (b) (5ab)3In the following exercises, simplify each expression using the Product Property for Exponents. 121. (a) (7n)3 (b) (3xyz)4In the following exercises, simplify each expression. 122. (a) (y2)4(y3)2 (b) (10a2b)3In the following exercises, simplify each expression. 123. (a) (w4)3(w5)2 (b) (2xy4)5In the following exercises, simplify each expression. 124. (a) (2r3s2)4 (b) (m5)3(m9)4In the following exercises, simplify each expression. 125. (a) (10q2p4)3 (b) (n3)10(n5)2In the following exercises, simplify each expression. 126. (a) (3x)2(5x) (b) (5t2)3(3t)2In the following exercises, simplify each expression. 127. (a) (2y)3(6y) (b) (10k4)3(5k6)2In the following exercises, simplify each expression. 128. (a) (5a)2(2a)3 (b) (12y2)3(23y)2In the following exercises, simplify each expression. 129. (a) (4b)2(3b)3 (b) (12j2)5(25j3)2In the following exercises, simplify each expression. 130. (a) (25x2y)3 (b) (89xy4)2In the following exercises, simplify each expression. 131. (a) (2r2)3(4r)2 (b) (3x3)3(x5)4In the following exercises, simplify each expression. 132. (a) (m2n)2(2mn5)4 (b) (3pq4)2(6p6q)2In the following exercises, multiply the monomials. 133. (6y7)(3y4)In the following exercises, multiply the monomials. 134. (10x5)(3x3)In the following exercises, multiply the monomials. 135. (8u6)(9u)In the following exercises, multiply the monomials. 136. (6c4)(12c)In the following exercises, multiply the monomials. 137. (15f8)(20f3)In the following exercises, multiply the monomials. 138. (14d5)(36d2)In the following exercises, multiply the monomials. 139. (4a3b)(9a2b6)In the following exercises, multiply the monomials. 140. (6m4n2)(7mn5)In the following exercises, multiply the monomials. 141. (47rs2)(14rs3)In the following exercises, multiply the monomials. 142. (58x3y)(24x5y)In the following exercises, multiply the monomials. 143. (23x2y)(34xy2)In the following exercises, multiply the monomials. 144. (35m3n2)(59m2n3)In the following exercises, multiply the monomials. 145. (x2)4(x3)2In the following exercises, multiply the monomials. 146. (y4)3(y5)2In the following exercises, multiply the monomials. 147. (a2)6(a3)8In the following exercises, multiply the monomials. 148. (b7)5(b2)6In the following exercises, simplify each expression. 149. (2m6)3In the following exercises, simplify each expression. 150. (3y2)4In the following exercises, simplify each expression. 151. (10x2y)3In the following exercises, simplify each expression. 152. (2mn4)5In the following exercises, simplify each expression. 153. (2a3b2)4In the following exercises, simplify each expression. 154. (10u2v4)3In the following exercises, simplify each expression. 155. (23x2y)3In the following exercises, simplify each expression. 156. (79pq4)2In the following exercises, simplify each expression. 157. (8a3)2(2a)4In the following exercises, simplify each expression. 158. (5r2)3(3r)2In the following exercises, simplify each expression. 159. (10p4)3(5p6)2In the following exercises, simplify each expression. 160. (4x3)3(2x5)4In the following exercises, simplify each expression. 161. (12x2y3)4 (4x5y3)2In the following exercises, simplify each expression. 162. (13m3n2)4(9m8n3)2In the following exercises, simplify each expression. 163. (3m2n)2(2mn5)4In the following exercises, simplify each expression. 164. (2pq4)(5p6q)2Email Kate emails a flyer to ten of her friends and tells them to forward it to ten of their friends, who forward it to ten of their friends, and so on. The number of people who receive the email on the second round is 102 , on the third round is 103 , as shown in the table below. How many people will receive the email on the sixth round? Simplify the expression to 1show the number of people who receive the email.Salary Jamal’s boss gives him a 3% raise every year on his birthday. This means that each year, Jamal’s salary is 1.03 times his last year’s salary. If his original salary was $35,000, his salary after 1 year was $35,000(1.03), after 2 years was $35,000(1.03)2, after 3 years was $35,000(1.03)3, as shown in the table below. What will Jamal’s salary be after 10 years? Simplify the expression, to show Jamal’s salary in dollars.Clearance A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week’s cost. If the original cost of a sofa was $1,000, the cost for the first week would be $1000(0.70) and the cost of the item during the second week would be $1,000(0.70)2. Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.Use the Product Property for Exponents to explain why xx=x2 .Explain why 53=(5)3 but 54(5)4 .Jorge thinks (12)2 is 1. What is wrong with his reasoning?Explain why x3x5 is x8 , and not x15 .Multiply: 5(x+7) .Multiply: 3(y+13) .Multiply: x(x7) .Multiply: d(d11) .Multiply: 5x(x+4y) .Multiply: 2p(6p+r) .Multiply: 3y(5y2+8y7) .Multiply: 4x2(2x23x+5) .Multiply: 4x(3x25x+3) .Multiply: 6a3(3a22a+6) .Multiply: (x+8)p .Multiply: (a+4)p .Multiply: (x+8)(x+9) .Multiply: (5x+9)(4x+3) .Multiply: (3b+5)(4b+6) .Multiply: (a+10)(a+7) .Multiply: (5y+2)(6y3) .Multiply: (3c+4)(5c2) .Multiply: (a+7)(ab) .Multiply: (x+5)(xy) .Multiply using the FOIL method: (x+6)(x+8) .Multiply using the FOIL method: (y+17)(y+3) .Multiply: (x7)(x+5) .Multiply: (b3)(b+6) .Multiply: (3x+7)(5x2) .Multiply: (4y+5)(4y10) .Multiply: (10cd)(c6) .Multiply: (7xy)(2x5) .Multiply: (x2+6)(x8) .Multiply: (y2+7)(y9) .Multiply: (2ab+5)(4ab4) .Multiply: (2xy+3)(4xy5) .Multiply using the Vertical Method: (5m7)(3m6) .Multiply using the Vertical Method: (6b5)(7b3) .Multiply using the Distributive Property: (y3)(y25y+2) .Multiply using the Distributive Property: (x+4)(2x23x+5) .Multiply using the Vertical Method: (y3)(y25y+2) .Multiply using the Vertical Method: (x+4)(2x23x+5) .In the following exercises, multiply. 173. 4(w+10)In the following exercises, multiply. 174. 6(b+8)In the following exercises, multiply. 175. 3(a+7)In the following exercises, multiply. 176. 5(p+9)In the following exercises, multiply. 177. 2(x7)In the following exercises, multiply. 178. 7(y4)In the following exercises, multiply. 179. 3(k4)In the following exercises, multiply. 180. 8(j5)In the following exercises, multiply. 181. q(q+5)In the following exercises, multiply. 182. k(k+7)In the following exercises, multiply. 183. b(b+9)In the following exercises, multiply. 184. y(y+3)In the following exercises, multiply. 185. x(x10)In the following exercises, multiply. 186. p(p15)In the following exercises, multiply. 187. 6r(4r+s)In the following exercises, multiply. 188. 5c(9c+d)In the following exercises, multiply. 189. 12x(x10)In the following exercises, multiply. 190. 9m(m11)In the following exercises, multiply. 191. 9a(3a+5)In the following exercises, multiply. 192. 4p(2p+7)In the following exercises, multiply. 193. 3(p2+10p+25)In the following exercises, multiply. 194. 6(y2+8y+16)In the following exercises, multiply. 195. 8(x2+2x15)In the following exercises, multiply. 196. 5(t2+3t18)In the following exercises, multiply. 197. 5q3(q32q+6)In the following exercises, multiply. 198. 4x3(x43x+7)In the following exercises, multiply. 199. 8y(y2+2y15)In the following exercises, multiply. 200. 5m(m2+3m18)In the following exercises, multiply. 201. 5q3(q22q+6)In the following exercises, multiply. 202. 9r3(r23r+15)In the following exercises, multiply. 203. 4z2(3z2+12z1)In the following exercises, multiply. 204. 3x2(7x2+10x1)In the following exercises, multiply. 205. (2m9)mIn the following exercises, multiply. 206. (8j1)jIn the following exercises, multiply. 207. (w6)8In the following exercises, multiply. 208. (k4)5In the following exercises, multiply. 209. 4(x+10)In the following exercises, multiply. 210. 6(y+8)In the following exercises, multiply. 211. 15(r24)In the following exercises, multiply. 212. 12(v30)In the following exercises, multiply. 213. 3(m+11)In the following exercises, multiply. 214. 4(p+15)In the following exercises, multiply. 215. 8(z5)In the following exercises, multiply. 216. 3(x9)In the following exercises, multiply. 217. u(u+5)In the following exercises, multiply. 218. q(q+7)In the following exercises, multiply. 219. n(n23n)In the following exercises, multiply. 220. s(s26s)In the following exercises, multiply. 221. 6x(4x+y)In the following exercises, multiply. 222. 5a(9a+b)In the following exercises, multiply. 223. 5p(11p5p)In the following exercises, multiply. 224. 12u(3u4v)In the following exercises, multiply. 225. 3(v2+10v+25)In the following exercises, multiply. 226. 6(x2+8x+16)In the following exercises, multiply. 227. 2n(4n24n+1)In the following exercises, multiply. 228. 3r(2r26r+2)In the following exercises, multiply. 229. 8y(y2+2y15)In the following exercises, multiply. 230. 5m(m2+3m18)In the following exercises, multiply. 231. 5q3(q22q+6)In the following exercises, multiply. 232. 9r3(r23r+5)In the following exercises, multiply. 233. 4z2(3z2+12z1)In the following exercises, multiply. 234. 3x2(7x2+10x1)In the following exercises, multiply. 235. (2y9)yIn the following exercises, multiply. 236. (8b1)bIn the following exercises, multiply the following binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 237. (w+5)(w+7)In the following exercises, multiply the following binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 238. (y+9)(y+3)In the following exercises, multiply the following binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 239. (p+11)(p4)In the following exercises, multiply the following binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 240. (q+4)(q8)In the following exercises, multiply the binomials. Use any method. 241. (x+8)(x+3)In the following exercises, multiply the binomials. Use any method. 242. (y+7)(y+4)In the following exercises, multiply the binomials. Use any method. 243. (y6)(y2)In the following exercises, multiply the binomials. Use any method. 244. (x7)(x2)In the following exercises, multiply the binomials. Use any method. 245. (w4)(w+7)In the following exercises, multiply the binomials. Use any method. 246. (q5)(q+5)In the following exercises, multiply the binomials. Use any method. 247. (p+12)(p5)In the following exercises, multiply the binomials. Use any method. 248. (m+11)(m4)In the following exercises, multiply the binomials. Use any method. 249. (6p+5)(p+1)In the following exercises, multiply the binomials. Use any method. 250. (7m+1)(m+3)In the following exercises, multiply the binomials. Use any method. 251. (2t9)(10t+1)In the following exercises, multiply the binomials. Use any method. 252. (3r8)(11r+1)In the following exercises, multiply the binomials. Use any method. 253. (5xy)(3x6)In the following exercises, multiply the binomials. Use any method. 254. (10ab)(3a4)In the following exercises, multiply the binomials. Use any method. 255. (a+b)(2a+3b)In the following exercises, multiply the binomials. Use any method. 256. (r+s)(3r+2s)In the following exercises, multiply the binomials. Use any method. 257. (4zy)(z6)In the following exercises, multiply the binomials. Use any method. 258. (5xy)(x4)In the following exercises, multiply the binomials. Use any method. 259. (x2+3)(x+2)In the following exercises, multiply the binomials. Use any method. 260. (y24)(y+3)In the following exercises, multiply the binomials. Use any method. 261. (x2+8)(x25)In the following exercises, multiply the binomials. Use any method. 262. (y27)(y24)In the following exercises, multiply the binomials. Use any method. 263. (5ab1)(2ab+3)In the following exercises, multiply the binomials. Use any method. 264. (2xy+3)(3xy+2)In the following exercises, multiply the binomials. Use any method. 265. (6pq3)(4pq5)In the following exercises, multiply the binomials. Use any method. 266. (3rs7)(3rs4)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 267. (x+5)(x2+4x+3)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 268. (u+4)(u2+3u+2)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 269. (y+8)(4y2+y7)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 270. (a+10)(3a2+a5)In the following exercises, multiply. Use either method. 271. (w7)(w29w+10)In the following exercises, multiply. Use either method. 272. (p4)(p26p+9)In the following exercises, multiply. Use either method. 273. (3q+1)(q24q5)In the following exercises, multiply. Use either method. 274. (6r+1)(r27r9)In the following exercises, multiply. Use either method. 275. (10y6)+(4y7)In the following exercises, multiply. Use either method. 276. (15p4)+(3p5)In the following exercises, multiply. Use either method. 277. (x24x34)(x2+7x6)In the following exercises, multiply. Use either method. 278. (j28j27)(j2+2j12)In the following exercises, multiply. Use either method. 279. 5q(3q26q+11)In the following exercises, multiply. Use either method. 280. 8t(2t25t+6)In the following exercises, multiply. Use either method. 281. (s7)(s+9)In the following exercises, multiply Use either method. 282. (x5)(x+13)In the following exercises, multiply Use either method. 283. (y22y)(y+1)In the following exercises, multiply Use either method. 284. (a23a)(4a+5)In the following exercises, multiply Use either method. 285. (3n4)(n2+n7)In the following exercises, multiply Use either method. 286. (6k1)(k2+2k4)In the following exercises, multiply Use either method. 287. (7p+10)(7p10)In the following exercises, multiply Use either method. 288. (3y+8)(3y8)In the following exercises, multiply Use either method. 289. (4m23m7)m2In the following exercises, multiply Use either method. 290. (15c24c+5)c4In the following exercises, multiply Use either method. 291. (5a+7b)(5a+7b)In the following exercises, multiply Use either method. 292. (3x11y)(3x11y)In the following exercises, multiply Use either method. 293. (4y+12z)(4y12z)Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 13 times 15. Think of 13 as 10+3 and 15 as 10+5 . (a) Multiply (10+3)(10+5) by the FOIL method. (b) Multiply 1315 without using a calculator. (c) Which way is easier for you? Why?Mental math You can use binomial multiplication to multiply numbers without a calculator. Say you need to multiply 18 times 17. Think of 18 as 202 and 17 as 203 . (a) Multiply (202)(203) by the FOIL method. (b) Multiply 1817 without using a calculator. (c) Which way is easier for you? Why?Which method do you prefer to use when multiplying two binomials: the Distributive Property, the FOIL method, or the Vertical Method? Why?Which method do you prefer to use when multiplying a trinomial by a binomial: the Distributive Property or the Vertical Method? Why?Multiply the following: (x+2)(x2)(y+7)(y7)(w+5)(w5) Explain the pattern that you see in your answers.Multiply the following: (m3)(m+3)(n10)(n+10)(p8)(p+8) Explain the pattern that you see in your answers.Multiply the following: (p+3)(p+3)(q+6)(q+6)(r+1)(r+1) Explain the pattern that you see in your answers.Multiply the following: (x4)(x4)(y1)(y1)(z7)(z7) Explain the pattern that you see in your answers.