1 ESERCIZI Operare con numeri e lettere PER ESERCITARSI CON GRADUALIT Dopo averli scomposti in fattori, calcola il MCD e il mcm di ognuno dei seguenti insiemi di polinomi. 444 ab2 ab a3 + a2b 445 x2 + x x3y + x2 xy3 446 2x 2y 6x2 6y2 447 x2 4 x 2 448 x2 + x x2 + 2x + 1 449 9a2 b2 9a2 6ab + b2 450 2a2 + 10ab ab + 5b2 a2b2 451 t2 16 st 4s 5t 20 452 8a3 + 12a2b + 6ab2 + b3 20a + 10b 453 16x4 y4 4x2 + 4xy + y2 454 2a + 6 ax 3x 4 x2 455 3x2 3x 9x2 18x + 9 x2 1 [x 1; 9x(x 1)2(x + 1)] 456 x2 xy x3 + x2y xy2 y3 x2y + y3 2xy2 [x y; xy(x y)2(x + y)2] 457 2a2b2 2ab3 4a4b2 8a3b3 + 4a2b4 2a3b2 2ab4 458 3a2 3ab ab + b2 3a3 + 6a2b [a; a2b2(a + b)] [x; x2y3(x + 1)(xy + 1)] [2(x y): 6(x y)(x + y)] [x 2; (x 2)(x + 2)] x+1 [x + 1; x(x + 1)2] [3a b; (3a b)2(3a + b)] [1; 2a2b2(a + 5b)] [t 4; 5s(t 4)(t + 4)] [2a + b; 10(2a + b)3] 4x2 4xy + y2 [1; (2x y)2 (2x + y)2 (4x2 + y2)] [2 x; (2 x)(2 + x)(a + 3)] [2ab2 (a b); 4a2b2 (a b)2(a + b)] [1; 3a2b(a + b)(a b)(a + 2b)] 459 2xy 36x3 + 24x2y + 4xy2 54x3y + 54x2y2 + 18xy3 + 2y4 [ ] 460 m2n2 m2n 3mn2 + 3mn m3 6m2 + 9m mn2 m 3n2 + 3 [ ] 461 7p3q3 + 14p2q3 + 7pq3 21p2 21 14p2q2 14p2q + 14pq2 14pq [ ] 462 2l2m 2lm2 l + m 2l2m 2lm2 2l2m 2lm2 + l m [ ] 463 2a3 12a2b + 24ab2 16b3 4a3 16a2b + 16ab2 6a2 12ab [ ] 464 x3 8 x2 4 465 27a3 b3 9a2 b2 9a2 6ab + b2 [ ] 466 x3 3x2y + 3xy2 y3 x2 xy x2 2xy + y2 [ ] 467 x4 6x3 + 12x2 8x x2 4 ax 2a + x 2 [ ] 468 q10r3s5 q7r3s5 q7r2s3 q5r2s3 q6r2s3 2q5r2s3 + q4r2s3 [ ] 469 27x2y5 27xy4 9x3y4 9x3y3 9x2y4 + 9x2y3 27x4y5 54x3y4 + 27x2y3 [ ] 470 18ax12 18ax9y3 9a2x9 + 9a2x8y + 9a2x7 27a2x9 + 54a2x8y + 27a2x7y2 [ ] 471 4a5b + 8a4b 60a3b 6a4b2 + 60a3b2 + 150a2b2 6a2 + 48a + 90 [ ] 472 3xy4 3xy3 + 27xy2 27xy 3x2y4 + 27x2y2 6xy4 + 108xy2 + 486x [ ] 473 a2 4ab + 2a + 4b2 4b + 1 a2 4ab + 4b2 1 [ ] [ ] 69