Working with Algebraic Expressions
3
(c) 3x(2x − 8) (d) 2x (x 2 − x + 7) (e) 4(x − 1) − 5(2x + 11) (f) 7x (x + 1) − 3x (x + 2) (g) 2x(x − 1) − 3(2x 2 − 5x + 9) (h) x (6x − 2) − (7x 2 − x − 11) (i) x 2(3x + 1) − 2x (3x 2 − x + 5) (j) −2x(x 2 − 1) + 3x 2(3x − 1)
5. Multiply out and simplify the following: (a) (x + 2)(x + 5)
(b) (3x + 7)(2x + 3) (c) ( y + 5)( y + 8) (d) (3x − 5)(2x − 1) (e) x (x − 3)(2x + 4) (f) (2x 2 + x + 1)(x + 1) (g) (x 2 − x + 5)(x − 3) (h) (x − 1)(3x 2 + 5x − 7) (i) (−2x 2 + 5x − 6)(1 − x) (j) (2x − 1)(x + 2)(x − 1)
6. Multiply out the following. The answers are a difference of two squares expression, which simplifi es the process.
(a) (x + 2)(x − 2) (b) (2x − 1)(2x + 1) (c) (4x − 1)(4x + 1) (d) (x 2 + 1)(x 2 − 1) (e) (3x − 2)(3x + 2)
(f) (4x − 3)(4x + 3) (g) (x 2 − 5)(x 2 + 5) (h) ( y − 3)( y + 3) (i) (3 + x)(3 – x) (j) (x + 2y)(x – 2y)
7. Multiply out the following perfect squares: (a) (x + 1)2 (b) (x + 2)2 (c) (2x + 1)2 (d) (3x + 2)2 (e) (x − 4)2 (f) (2x − 3)2
(g) (5x − 4)2 (h) (x 2 − 11)2 (i) (4x − 5)2 (j) (2x + 3y)2 (k) (ax − b)2 (l) (a + 1)2 − (a − 1)2
8. Multiply out and simplify the following: (a) (x − 2)(x + 1)(x + 2)
(b) (2x − 1)(x + 3)(2x + 1) (c) (2x + 3)(3x − 1)(2x − 3) (d) (x + 1)3
[Hint: (x + 1)2(x + 1)]
(e) (2x − 1)3 [Hint: (2x − 1)2(2x − 1)] (f) (x − 2)(2x + 1)(x − 3)
9. (a) If p = x + 5y − 3 and q = 2x − 3y + 7, fi nd the following, in terms of x and y:
(i) p + q (ii) p − q
(iii) 2p + 5q (iv) q − 2p
(b) If p = x + 3 and q = −2x + 5, fi nd the following, in terms of x:
(i) p + q (ii) p − q (iii) pq
(i) p + q (ii) p − q
(iv) ( p + q) 2 (v) ( p − q)2 (vi) p2 + q 2
(c) If p = 5x 2 − 2x + 1 and q = −3x 2 + x – 8, fi nd the following, in terms of x:
(iii) q − 2p (iv) 3p + 5q
10. Find the values of the following expressions: (a) x + 2y if x = 4 and y = 7
(b) 3x + 11y if x = −2 and y = 3⋅5 (c) 4x − 3y + 8 if x = −1 and y = −6 (d) 5x 2 if x = −3 (e) −5x 2 if x = −3 (f) (5x)2 if x = 3 (g) x 2 − 3y 2 if x = 3 and y = −2 (h) 2x 2 + 5x – 7 if x = 5 (i) −5x 2 + 7x – 3 if x = −2 (j) (2x + 3y)2 if x = −3 and y = 4 (k) 2x 2y − 3xy 2 – 7 if x = 3 and y = −2 (l) 3x 2y 2 − 5x + 7(x − y)2 if x = −2 and y = 0⋅5
61
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116 |
Page 117 |
Page 118 |
Page 119 |
Page 120 |
Page 121 |
Page 122 |
Page 123 |
Page 124 |
Page 125 |
Page 126 |
Page 127 |
Page 128 |
Page 129 |
Page 130 |
Page 131 |
Page 132 |
Page 133 |
Page 134 |
Page 135 |
Page 136 |
Page 137 |
Page 138 |
Page 139 |
Page 140 |
Page 141 |
Page 142 |
Page 143 |
Page 144 |
Page 145 |
Page 146 |
Page 147 |
Page 148 |
Page 149 |
Page 150 |
Page 151 |
Page 152 |
Page 153 |
Page 154 |
Page 155 |
Page 156 |
Page 157 |
Page 158 |
Page 159 |
Page 160 |
Page 161 |
Page 162 |
Page 163 |
Page 164 |
Page 165 |
Page 166 |
Page 167 |
Page 168 |
Page 169 |
Page 170 |
Page 171 |
Page 172 |
Page 173 |
Page 174 |
Page 175 |
Page 176 |
Page 177 |
Page 178 |
Page 179 |
Page 180 |
Page 181 |
Page 182 |
Page 183 |
Page 184 |
Page 185 |
Page 186 |
Page 187 |
Page 188 |
Page 189 |
Page 190 |
Page 191 |
Page 192 |
Page 193 |
Page 194 |
Page 195 |
Page 196 |
Page 197 |
Page 198 |
Page 199 |
Page 200 |
Page 201 |
Page 202 |
Page 203 |
Page 204 |
Page 205 |
Page 206 |
Page 207 |
Page 208 |
Page 209 |
Page 210 |
Page 211 |
Page 212 |
Page 213 |
Page 214 |
Page 215 |
Page 216 |
Page 217 |
Page 218 |
Page 219 |
Page 220 |
Page 221 |
Page 222 |
Page 223 |
Page 224 |
Page 225 |
Page 226 |
Page 227 |
Page 228 |
Page 229 |
Page 230 |
Page 231 |
Page 232 |
Page 233 |
Page 234 |
Page 235 |
Page 236 |
Page 237 |
Page 238 |
Page 239 |
Page 240 |
Page 241 |
Page 242 |
Page 243 |
Page 244 |
Page 245 |
Page 246 |
Page 247 |
Page 248 |
Page 249 |
Page 250 |
Page 251 |
Page 252 |
Page 253 |
Page 254 |
Page 255 |
Page 256 |
Page 257 |
Page 258 |
Page 259 |
Page 260 |
Page 261 |
Page 262 |
Page 263 |
Page 264 |
Page 265 |
Page 266 |
Page 267 |
Page 268 |
Page 269 |
Page 270 |
Page 271 |
Page 272 |
Page 273 |
Page 274 |
Page 275 |
Page 276 |
Page 277 |
Page 278 |
Page 279 |
Page 280 |
Page 281 |
Page 282 |
Page 283 |
Page 284 |
Page 285 |
Page 286 |
Page 287 |
Page 288 |
Page 289 |
Page 290 |
Page 291 |
Page 292 |
Page 293 |
Page 294 |
Page 295 |
Page 296 |
Page 297 |
Page 298 |
Page 299 |
Page 300 |
Page 301 |
Page 302 |
Page 303 |
Page 304 |
Page 305 |
Page 306 |
Page 307 |
Page 308 |
Page 309 |
Page 310 |
Page 311 |
Page 312 |
Page 313 |
Page 314 |
Page 315 |
Page 316 |
Page 317 |
Page 318 |
Page 319 |
Page 320 |
Page 321 |
Page 322 |
Page 323 |
Page 324 |
Page 325 |
Page 326 |
Page 327 |
Page 328 |
Page 329 |
Page 330 |
Page 331 |
Page 332 |
Page 333 |
Page 334 |
Page 335 |
Page 336 |
Page 337 |
Page 338 |
Page 339 |
Page 340 |
Page 341 |
Page 342 |
Page 343 |
Page 344 |
Page 345 |
Page 346 |
Page 347 |
Page 348 |
Page 349 |
Page 350 |
Page 351 |
Page 352 |
Page 353 |
Page 354 |
Page 355 |
Page 356 |
Page 357 |
Page 358 |
Page 359 |
Page 360 |
Page 361 |
Page 362 |
Page 363 |
Page 364 |
Page 365 |
Page 366
