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All Textbook Solutions for Elementary Algebra
Multiply: (x+9)2 .Multiply: (y+11)2 .Multiply: (x9)2 .Multiply: (p13)2 .Multiply: (6x+3)2 .Multiply: (4x+9)2 .Multiply: (2cd)2 .Multiply: (4x5y)2 .Multiply: (2x2+1)2 .Multiply: (3y3+2)2 .Multiply: (x5)(x+5) .Multiply: (w3)(w+3) .Multiply: (6x+5)(6x5) .Multiply: (2x+7)(2x7) .Multiply: (7+4x)(74x) .Multiply: (92y)(9+2y) .Find the product: ( 4p7q )( 4p+7q )Find the product: (3xy)(3x+y) .Find the product: (xy6)(xy+6) .Find the product: (ab9)(ab+9) .Find the product: (3x24y3)(3x2+4y3) .Find the product: Find the product: (3x24y3)(3x2+4y3) .Choose the appropriate pattern and use it to find the product: (a) (9b2)(2b+9) (b) (9p4)2 (c) (7y+1)2 (d) (4r3)(4r+3)Choose the appropriate pattern and use it to find the product: (a) (6x+7)2 (b) (3x4)(3x+4) (c) (2x5)(5x2) (d) (6n1)2In the following exercises, square each binomial using the Binomial Squares Pattern. 302. (w+4)2In the following exercises, square each binomial using the Binomial Squares Pattern. 303. (q+12)2In the following exercises, square each binomial using the Binomial Squares Pattern. 304. (y+14)2In the following exercises, square each binomial using the Binomial Squares Pattern. 305. (x+23)2In the following exercises, square each binomial using the Binomial Squares Pattern. 306. (b7)2In the following exercises, square each binomial using the Binomial Squares Pattern. 307. (y6)2In the following exercises, square each binomial using the Binomial Squares Pattern. 308. (m15)2In the following exercises, square each binomial using the Binomial Squares Pattern. 309. (p13)2In the following exercises, square each binomial using the Binomial Squares Pattern. 309. (3d+1)2In the following exercises, square each binomial using the Binomial Squares Pattern. 311. (4a+10)2In the following exercises, square each binomial using the Binomial Squares Pattern. 312. (2q+13)2In the following exercises, square each binomial using the Binomial Squares Pattern. 313. (3z+15)2In the following exercises, square each binomial using the Binomial Squares Pattern. 314. (3xy)2In the following exercises, square each binomial using the Binomial Squares Pattern. 315. (2y3z)2In the following exercises, square each binomial using the Binomial Squares Pattern. 316. (15x17y)2In the following exercises, square each binomial using the Binomial Squares Pattern. 317. (18x19y)2In the following exercises, square each binomial using the Binomial Squares Pattern. 318. (3x2+2)2In the following exercises, square each binomial using the Binomial Squares Pattern. 319. (5u2+9)2In the following exercises, square each binomial using the Binomial Squares Pattern. 320. (4y32)2In the following exercises, square each binomial using the Binomial Squares Pattern. 321. (8p23)2In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 322. (m7)(m+7)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 323. (c5)(c+5)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 324. (x+34)(x34)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 325. (b+67)(b67)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 326. (5k+6)(5k6)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 327. (8j+4)(8j4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 328. (11k+4)(11k4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 329. (9c+5)(9c5)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 330. (11bb)(11+b)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 331. (13q)(13+q)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 332. (53x)(5+3x)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 323. (46y)(4+6y)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 334. (9c2d)(9c+2d)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 335. (7w+10x)(7w10x)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 336. (m+23n)(m23n)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 337. (p+45q)(p45q)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 338. (ab4)(ab+4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 339. (xy9)(xy+9)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 340. (uv35)(uv+35)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 341. (rs27)(rs+27)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 342. (2x23y4)(2x2+3y4)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 343. (6m34n5)(6m3+4n5)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 344. (12p311q2)(12p3+11q2)In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern. 345. (15m28n4)(15m2+8n4)In the following exercises, find each product. 346. (a) (p3)(p+3) (b) (t9)2 (c) (m+n)2 (d) (2x+y)(x2y)In the following exercises, find each product. 347. (a) (2r+12)2 (b) (3p+8)(3p8) (c) (7a+b)(a7b) (d) (k6)2In the following exercises, find each product. 348. (a) (a57b)2 (b) (x2+8y)(8xy2) (c) (r6+s6)(r6s6) (d) (y4+2z)2In the following exercises, find each product. 349. (a) (x5+y5)(x5y5) (b) (m38n)2 (c) (9p+8q)2 (d) (r2s3)(r3+s2)Mental math You can use the product of conjugates pattern to multiply numbers without a calculator. Say you need to multiply 47 times 53. Think of 47 as 503and 53 as 50+3. (a) Multiply (503)(50+3) by using the product of conjugates pattern, (ab)(a+b)=a2b2. (b) Multiply 4783without using a calculator. (c) Which way is easier for you? Why?Mental math You can use the binomial squares pattern to multiply numbers without a calculator. Say you need to square 65. Think of 65 as 60+5. (a) Multiply (60+5)2 by using the binomial squares pattern (a+b)2=a2+2ab+b2 . (b) Square 65 without using a calculator. (c) Which way is easier for you? Why?How do you decide which pattern to use?Why does (a+b)2result in a trinomial. but (a+b)(ab)result in a binomial?Marta did the following work on her homework paper: a. (3y)2 b. 32y2 c. 9y2 Explain what is wrong with Marta’s work.Use the order of operations to show that (3+5)2is 64, and then use that numerical example to explain why (a+b)2a2+b2 .Simplify: (a) x15x10 (b) 61465Simplify: (a) y43y37 (b) 1015107Simplify: (a) x18x22 (b) 12151230Simplify: (a) m7m15 (b) 98919Simplify: (a) b19b11 (b) z5z11Simplify: (a) p9p17 (b) w13w9Simplify: (a) 150 (b) m0Simplify: (a) k0 (b) 290Simplify: (a) (11z)0 (b) (11pq3)0 .Simplify: (a) (6d)0 (b) (8m2n3)0Simplify: (a) (58)2 (b) (p 10)4 (c) (mn)4 .Simplify: (a) (13)3 (b) ( 2q)3 (c) (wx)4Simplify: (m5)4m7 .Simplify: (k2)6k7Simplify: n12(n3)4 .Simplify: x15(x3)5Simplify: ( r 5 r 3 )4Simplify: ( v 6 v 4 )3Simplify: ( a 3 b 2 )4Simplify: ( q 7 r 5 )3Simplify: ( 7 x 3 9y)2Simplify: ( 3 x 4 7y)2 .Simplify: (a2)3(a2)4(a4)5Simplify: (p3)4(p5)3(p7)6Simplify: (3r3)2(r3)7(r3)3Simplify: (2x4)5(4x3)2(x3)5Find the quotient: 42y96y3 .Find the quotient: 48z88z2 .Find the quotient: 72a7b38a12b4Find the quotient: 63c8d37c12d2 .Find the quotient: 16a7b624ab8Find the quotient: 27p4q745p12qFind the quotient: 28x5y1449x9y12Find the quotient: 30m5n1148m10n14 .Find the quotient: (6a4b5)(4a2b5)12a5b8Find the quotient: (12x6y9)(4x5y8)12x10y12In the following exercises, simplify. 356. (a) x18x3 (b) 51253In the following exercises, simplify. 357. (a) y20y10 (b) 71672 .In the following exercises, simplify. 358. (a) p21p7 (b) 41644In the following exercises, simplify. 359. (a) u24u3 (b) 91595In the following exercises, simplify. 360. (a) q18q36 (b) 102103In the following exercises, simplify. 361. (a) t10t40 (b) 8385In the following exercises, simplify. 362. (a) bb9 (b) 446In the following exercises, simplify. 363. (a) xx7 (b) 10103In the following exercises, simplify. 364. (a) 20º (b) bºIn the following exercises, simplify. 365. (a) 13 (b) kIn the following exercises, simplify. 366. (a) 27 (b) (27)In the following exercises, simplify. 367. (a) 15 (b) (15)In the following exercises, simplify. 368. (a) (25x) (b) 25xIn the following exercises, simplify. 369. (a) (6y) (b) 6yIn the following exercises, simplify. 370. (a) (12x) (b) (56p4q3)In the following exercises, simplify. 371. (a) 7y0(17y)0 (b) (93c7d15)0In the following exercises, simplify. 372. (a) 12n018m0 (b) (12n)0(18m)0In the following exercises, simplify. 373. (a) 15r022s0 (b) (15r)0(22s)0In the following exercises, simplify. 343. (a) (34)3 (b) (p2)5 (c) (xy)6In the following exercises, simplify. 375. (a) (25)2 (b) (x3)4 (c) (ab)5In the following exercises, simplify. 376. (a) (a 3b)4 (b) (5 4m)2In the following exercises, simplify. 377. (a) (x 2y)3 (b) ( 10 3q)4In the following exercises, simplify. 378. (a2)3a4In the following exercises, simplify. 379. (p3)4p5In the following exercises, simplify. 380. (y3)4y10wIn the following exercises, simplify. 381. (x4)5x15In the following exercises, simplify. 382. u6(u3)2In the following exercises, simplify. 383. v20(v4)5In the following exercises, simplify. 384. m12(m8)3In the following exercises, simplify. 385. n8(n6)4In the following exercises, simplify. 386. ( p 9 p 3 )5In the following exercises, simplify. 387. ( q 8 q 2 )3In the following exercises, simplify. 388. ( r 2 r 6 )3In the following exercises, simplify. 389. ( m 4 m 7 )4In the following exercises, simplify. 390. (p r 11 )2In the following exercises, simplify. 391. (a b 6 )3In the following exercises, simplify. 392. ( w 5 x 3 )8In the following exercises, simplify. 393. ( y 4 z 10 )5In the following exercises, simplify. 394. ( 2 j 3 3k)4In the following exercises, simplify. 395. ( 3 m 5 5n)3In the following exercises, simplify. 396. ( 3 c 2 4 d 6 )3In the following exercises, simplify. 397. ( 5 u 7 2 v 3 )4In the following exercises, simplify. 398. ( k 2 k 8 k 3 )2In the following exercises, simplify. 399. ( j 2 j 5 j 4 )3In the following exercises, simplify. 400. (t2)5(t4)2(t3)7In the following exercises, simplify. 401. (q3)6(q2)3(q4)8In the following exercises, simplify. 402. (2p2)4(3p4)2(6p3)2In the following exercises, simplify. 403. (2k2)2(6k2)4(9k4)2In the following exercises, simplify. 404. (4m3)2(5m4)3(10m6)3In the following exercises, simplify. 405. (10n2)3(4n5)2(2n8)2In the following exercises, divide the monomials. 406. 56b87b2In the following exercises, divide the monomials. 407. 63v109v2In the following exercises, divide the monomials. 408. 88y158y3In the following exercises, divide the monomials. 409. 72u1212u4In the following exercises, divide the monomials. 410. 45a6b815a10b2In the following exercises, divide the monomials. 411. 54x9y318x6y15In the following exercises, divide the monomials. 412. 15r4s918r9s2In the following exercises, divide the monomials. 413. 20m8n430m5n9In the following exercises, divide the monomials. 414. 18a4b827a9b5In the following exercises, divide the monomials. 415. 45x5y960x8y6In the following exercises, divide the monomials. 416. 64q11r9s348q6r8s5In the following exercises, divide the monomials. 417. 65a10b8c542a7b6c8In the following exercises, divide the monomials. 418. (10m5n4)(5m3n6)25m7n5In the following exercises, divide the monomials. 419. (18p4q7)(6p3q8)36p12q10In the following exercises, divide the monomials. 420. (6a4b3)(4ab5)(12a2b)(a3b)In the following exercises, divide the monomials. 421. (4u2v5)(15u3v)(12u3v)(u4v)(a) 24a5+2a5 (b) 24a52a5 (c) 24a52a5 (d) 24a52a5(a) 15n10+3n10 (b) 15n103n10 (c) 15n103n10 (d) 15n103n10(a) p4p6 (b) (p4)6(a) q5q3 (b) (q5)3(a) y3y (b) yy3(a) z6z5 (b) z5z6(8x5)(9x)6x3(4y)(12y7)8y227a73a3+54a99a532c114c5+42c96c332y58y2+60y105y748x66x435x97x763r6s39r4s272r2s26s56y4z57y3z345y2z25yMemory One megabyte is approximately 106 bytes. One gigabyte is approximately 109 bytes. How many megabytes are in one gigabyte?Memory One gigabyte is approximately 109 bytes. One terabyte is approximately 1012 bytes. How many gigabytes are in one terabyte?Jennifer thinks the quotient a24a6 simplifies to a4 . What is wrong with her reasoning?Maurice simplifies the quotient d7d by writing d7d=7 . What is wrong with his reasoning?When Drake simplified 30 and (3)0 he got the same answer. Explain how using the Order of Operations correctly gives different answers.Robert thinks x0 simplifies to 0. What would you to convince Robert he is wrong?Find the quotient: 8z2+244Find the quotient: 18z2279Find the quotient: (27b233b2)3bFind the quotient: (25y355y2)5y .Find the quotient: 25y215y5Find the quotient: 42b218b6Find the quotient: 60d7+24d54d3Find the quotient: 216p748p56p3Find the quotient: (32a2b16ab2)(8ab) .Find the quotient: (48a8b436a6b5)(6a3b3) .Find the quotient: 40x3y2+24x2y216x2y38x2yFind the quotient: 35a4b2+14a4b242a2b47a2b2Find the quotient: 18c2+6c96cFind the quotient: 10d25d25dFind the quotient: (y2+10y+21)(y+3) .Find the quotient: (m2+9m+20)(m+4)Find the quotient: (2x23x20)(x4) .Find the quotient: (3x216x12)(x6) .Find the quotient: (x3+5x2+8x+6)(x+2) .Find the quotient: (2x3+8x2+x8)(x+1) .Find the quotient: (x3+3x+14)(x+2) .Find the quotient: (x43x31000)(x+5) .Find the quotient: (x364)(x4) .Find the quotient: 25x38)(5x2) .In the following exercises, divide each polynomial by the monomial. 442. 45y+369In the following exercises, divide each polynomial by the monomial. 443. 30b+755In the following exercises, divide each polynomial by the monomial. 444. 8d24d2In the following exercises, divide each polynomial by the monomial. 445. 42x214x7In the following exercises, divide each polynomial by the monomial. 446. (16y220y)4yIn the following exercises, divide each polynomial by the monomial. 447. (55w210w)5wIn the following exercises, divide each polynomial by the monomial. 448. (9n4+6n3)3nIn the following exercises, divide each polynomial by the monomial. 449. (8x3+6x2)2xIn the following exercises, divide each polynomial by the monomial. 450. 18y212y6In the following exercises, divide each polynomial by the monomial. 451. 20b212b4In the following exercises, divide each polynomial by the monomial. 452. 35a4+65a25In the following exercises, divide each polynomial by the monomial. 453. 51m4+72m33In the following exercises, divide each polynomial by the monomial. 454. 310y4200y35y2In the following exercises, divide each polynomial by the monomial. 454. 412z848z54z3In the following exercises, divide each polynomial by the monomial. 456. 46x338x22x2In the following exercises, divide each polynomial by the monomial. 457. 51y4+42y23y2In the following exercises, divide each polynomial by the monomial. 458. (24p233p)(3p)In the following exercises, divide each polynomial by the monomial. 459. (35x421x)(7x)In the following exercises, divide each polynomial by the monomial. 460. (63m442m3)(7m2)In the following exercises, divide each polynomial by the monomial. 461. (48y424y3)(8y2)In the following exercises, divide each polynomial by the monomial. 462. (63a2b3+72ab4)(9ab)In the following exercises, divide each polynomial by the monomial. 463. (45x3y4+60xy2)(5xy)In the following exercises, divide each polynomial by the monomial. 464. 52p5q4+36p4q364p3q24pqIn the following exercises, divide each polynomial by the monomial. 465. 49c2d270c3d335c2d47cd2In the following exercises, divide each polynomial by the monomial. 466. 66x3y2110x2y344x4y311x2y2In the following exercises, divide each polynomial by the monomial. 467. 72r5s2+132r4s396r3s512r2s2In the following exercises, divide each polynomial by the monomial. 468. 4w2+2w52wIn the following exercises, divide each polynomial by the monomial. 469. 12q2+3q13qIn the following exercises, divide each polynomial by the monomial. 470. 10x2+5x45xIn the following exercises, divide each polynomial by the monomial. 471. 20y2+12y14yIn the following exercises, divide each polynomial by the monomial. 472. 36p3+18p212p6p2In the following exercises, divide each polynomial by the monomial. 473. 63a3108a2+99a9a2In the following exercises, divide each polynomial by the monomial. 474. (y2+7y+12)(y+3)In the following exercises, divide each polynomial by the monomial. 475. (d2+8d+12)(d+2)In the following exercises, divide each polynomial by the monomial. 476. (x23x10)(x+2)In the following exercises, divide each polynomial by the monomial. 477. (a22a35)(a+5)In the following exercises, divide each polynomial by the monomial. 478. (r212t+36)(t6)In the following exercises, divide each polynomial by the monomial. 479. (x214x+49)(x7)In the following exercises, divide each polynomial by the monomial. 480. (6m219m20)(m4)In the following exercises, divide each polynomial by the monomial. 481. (4x217x15)(x5)In the following exercises, divide each polynomial by the monomial. 482. (q2+2q+20)(q+6)In the following exercises, divide each polynomial by the monomial. 483. (p2+11p+16)(p+8)In the following exercises, divide each polynomial by the monomial. 484. (y23y15)(y8)In the following exercises, divide each polynomial by the monomial. 485. (x2+2x30)(x5)In the following exercises, divide each polynomial by the binomial. 486. (3b3+b2+2)(b+1)In the following exercises, divide each polynomial by the binomial. 487. (2n310n+24)(n+3)In the following exercises, divide each polynomial by the binomial. 488. (2y36y36)(y3)In the following exercises, divide each polynomial by the binomial. 459. (7q35q2)(q1)In the following exercises, divide each polynomial by the binomial. 490. (z3+1)(z+1)In the following exercises, divide each polynomial by the binomial. 491. (m3+1000)(m+10)In the following exercises, divide each polynomial by the binomial. 492. (a3125)(a5)In the following exercises, divide each polynomial by the binomial. 493. (x3216)(x6)In the following exercises, divide each polynomial by the binomial. 494. (64x327)(4x3)In the following exercises, divide each polynomial by the binomial. 495. (125y364)(5y4)Average cost Pictures Plus produces digital albums. The company’s average cost (in dollars) to make x albums is given by the expression 7x+500x . (a) Find the quotient by dividing the numerator by the denominator (b) What will the average cost (in dollars) be to produce 20 albums?Handshakes At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression n2n2 , where n represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?James divides 48y+6 4 by 6 this way : 48y+66=48y . What is wrong with his reasoning?Divide 10x2+x122x and explain with words how you get each term of the quotient.Simplify: (a) 23 (b) 107Simplify: (a) 32 (b) 104Simplify: (a) 1p8 (b) 143 .Simplify: (a) 1q7 (b) 124 .Simplify: (a) (23)4 (b) ( 6mn)2 .Simplify: (a) (35)3 (b) (a 2b)4Simplify: (a) 52 (b) 52 (c) (15)2 (d) (15)2Simplify: (a) (7)2 (b) 72 (c) (17)2 (d) (17)2Simplify: (a) 631 (b) (63)1Simplify: (a) 822 (b) (82)2Simplify: (a) y7 (b) (z3)5Simplify: (a) p9 (b) (q4)6 .Simplify: (a) 8p1 (b) (8p)1 (c) (8p)1 .Simplify: (a) 11q1 (b) (11q)1 (c) (11q)1 (c) (11q)1 .Simplify: (a) (x3)x7 (b) y7y2 (c) z4z5Simplify: (a) a1a6 (b) b8b4 (c) c8c7 .Simplify: (p6q2)(p9q1)Simplify: (r5s3)(r7s5)