ARITMETICA E ALGEBRA 450 (a + b + c)(a + b c) (a b + c)( a b + c) [2a2 2c2 + 2ab + 2bc] Completa con i segni + oppure , in modo che il risultato sia quello indicato a fianco. _1_ _1_ _1_ _1_ 451 (........... 2 a ........... 3 b)(........... 2 a ........... 3 b) 452 (........... 2 a ........... b)(........... 2 a ........... b) _1_ [ ] 1 1 risultato: __a2 __b2 4 9 _1_ 1 risultato: __a2 ab + b2 4 453 (........... a ........... b ........... c)(........... a ........... b ........... c) risultato: a2 b2 c2 + 2bc Calcola i seguenti prodotti (somma per differenza). 454 (a + b)(a b) (4p + 2)(4p 2) [a2 b2; 16p2 4] 455 (x + 5)(x 5) (3x + p)(3x p) [x2 25; 9x2 p2] 456 (2x + 3y)(2x 3y) ( 2x 3y)( 2x + 3y) [4x2 9y2; 4x2 9y2] 457 ( 3x2y + 1)(3x2y + 1) (a3b2 b)(a3b2 + b) [1 9x4y2; a6b4 b2] 458 (4a2y4 9)( 4a2y4 9) (5c + a2c)(a2 5c) [ 16a4y8 + 81; a4c2 25c2] 459 ( 3a3 5b)( 3a3 + 5b) ( 7x2y + 4xy3z)(7x2y + 4xy3z) 460 (5a2b + 7ab2)( 5a2b + 7ab2) ( ab2 a2b)( ab2 + a2b) 461 (xy2z3 + x3y2z)(x3y2z xy2z3) (2a2b + 1)(1 2a2b) _3_ _3_ [9a6 25b2; 49x4y2 + 16x2y6z2] [ 25a4b2 + 49a2b4; a2b4 a4b2] [x6y4z2 x2y4z6; 1 4a4b2] 462 (2 xy 2x)(2 xy + 2x) _2_ 2 _2_ 2 ( 3 a b 4c)( 3 a b + 4c) 463 _3_ 2 _3_ 2 (2 ab 1)(2 ab + 1) _2_ 3 _1_ _2_ 3 _1_ (3 ab 5)(3 ab + 5) 464 _3_ 3 _1_ 2 _3_ 3 _1_ 2 (4 xz 2 x y)(4 xz + 2 x y) 9 2 6 _1_ 4 2 ___ 1 2 2 4 ___ 25 6 4 2 2 _1_ 2 _5_ 3 2 _1_ _5_ 3 2 ___ (7 a b c + 5 abc )(5 abc 7 a b c) [ 16 x z 4 x y ; 25 a b c 49 a b c ] 465 2 2 _1_ _1_ (c d 4 c)(c d + 4 c) _3_ 3 _3_ 3 ( 4 a b)( 4 a + b) 466 _5_ 4 _5_ 4 ( 6 xy + 1)(6 xy + 1) _1_ 2 _1_ 2 _1_ 2 _1_ 2 (2 x y + 2 xy )(2 xy 2 x y) 25 2 8 _1_ 2 4 _1_ 4 2 ___ [1 36 x y ; 4 x y 4 x y ] 467 4 4 _1_ 3 _1_ 3 ( 2 a + 2a )( 2 a 2a ) _3_ 2 _2_ 2 _3_ 2 _2_ 2 (5 xy 3 x y)(5 xy + 3 x y) 9 2 4 _4_ 4 2 8 ___ _1_ 6 [ 4 a 4a ; 25 x y 9 x y ] 468 _3_ 3 _3_ 3 (2 a c)(2 a + c) (3 xy + 3 x)( 3 x + 3 xy) 469 3 2 3 2 ___ ___ (1 10 ab c)( 1 10 ab c) _3_ 3 2 _5_ _3_ 3 2 _5_ (2 s t n 4 t)(2 s t n + 4 t) 470 (an + b)(an b) _4_ _4_ _4_ (an bn)( an bn) _4_ con n N 471 (x + y)(x y)(x2 + xy + y2)(x2 xy + y2) (x3 + y3)(x3 y3) 472 (a2(a2 + a + 1) + a + 1)(a 1) (a3 + 1)(a2 1) _1_ _1_ _1_ _1_ _1_ _1_ 1 2 ___ 9 6 4 2 2 ___ [c d 16 c ; 16 a b ] 16 2 2 ___ 16 2 2 ___ _9_ 6 [4 a c ; 9 x y 9 x ] 9 2 4 2 25 2 ____ _9_ 6 4 2 ___ [ 100 a b c 1; 4 s t n 16 t ] [a2n b2; b2n a2n] [0] 91 2 ____ [ 900 x ] _1_ _1_ (1 + 2 x 3 y)(1 + 2 x + 3 y) (3 2 x y)(3 2 x + y) 475 (0,¯ 6a2b a)(0,¯ 6a2b + a) (0,5a)2(ab 1,5)(ab + 1,5) 356 1 _9_ 2 4 _4_ 2 6 ___ [ 4 a b 1; 9 a b 25 ] [a3 a2] 473 (0,1x y)(0,1x + y) + (y + 0,¯ 3x)(y 0,¯ 3x) 474 2 _4_ 4 2 2 _9_ 2 2 [ 4 x y 4x ; 9 a b 16c ] _8_ 2 _4_ _8_ [9y + 3x + 9] 7 4 2 ___ 7 2 ___ [ 36 a b 16 a ]