ARITMETICA E ALGEBRA 6.3 Il quadrato di un trinomio Calcola i seguenti quadrati di trinomi. esercizio svolto (2x2 + 3y3 5xy)2 Applichiamo la formula dello sviluppo del quadrato del trinomio: (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc Occorre tenere conto dei segni per i doppi prodotti. Otteniamo quindi: 4x4 + 9y6 + 25x2y2 + 12x2y3 20x3y 30x4y 496 (3m 2n + p)2 ( x y + z)2 497 (a2 + 3 3b)2 (m3 + m2 1)2 498 (2x y x3)2 ( a b c)2 499 (a2 + 2a3 + 4a4)2 ( 3a2 7ab + 4b2)2 [16a8 + 16a7 + 12a6 + 4a5 + a4; 9a4 + 25a2b2 + 16b4 56ab3 + 42a3b] _1_ + _x_ y 2 [a4 + 9 + 9b2 + 6a2 18b 6a2b; m6 + m4 + 1 + 2m5 2m2 2m3] [4x2 + y2 + x6 4xy 4x4 + 2x3y; a2 + b2 + c2 + 2ab + 2ac + 2bc] 2 _x_ _1_ ( 4 y 2) 500 (4 501 _1_ 2 _1_ 3 (x + 2 x 4 x ) 502 _1_ (4a 3b 2 c) 503 _3_ (2x + y 5 z) 504 _1_ 3 ( 2 x y + z) 505 _1_ 2 _1_ _1_ ( 2 xy + 4 x + 8) 2 [9m2 + 4n2 + p2 12mn 4np + 6mp; x2 + y2 + z2 + 2xy 2xz 2yz] ) 2 1 2 _1_x3 _1_x2 1 (2 2 4 2 2 2 4 1 1 1 2 2 3 3 8 6 4 3 4 5 _1_ 6 _1_ 2 2 [ 4 x + y + z + x y x z 2yz; x + 4y + 4 x y 4x y 2xy + x y] 2 _1_xy2 _1_x + _1_y (2 1 9 2 12 9 2 12 2 2 2 2 ___ _6_ ___ ___ _6_ ___ [4x + y + 25 z + 4xy 5 yz 5 xz; 4x + y + 25 z + 4xy + 5 yz + 5 xz] 4 3 _1_ (x 2y + 2 xy) 2 1 1 _4_ 3 2 2 2 _1_ 2 _4_ 6 ___ _1_ 3 _1_ [16a + 9b + 4 c 4ac + 3bc 24ab; 9 a + b + 16 3 a b 3 a + 2 b] _3_ ( 2x y 5 z) 2 1 1 6 _1_ 5 _1_ 4 1 4 3 2 _1_ 6 3 ___ ___ _1_ 5 _1_ 2 [ 16 x 4 x 4 x + x + x ; 4 x + 16 x + 1 4 x x + 2 x ] ) _2_ 3 _1_ ( 3 a + b + 4) 2 x2 2 2 ___ __ __ __ ___ 2 __ 6 __ __ [ 16 + 4 + y + 4 x 2 y xy; 16 x + y + 4 a + 4 x + 2 xy + y] 8 ) 1 2 ___ 1 ___ 1 2 ___ 1 2 _1_ 2 2 _1_ 3 ___ 1 1 _1_ 2 4 ___ _1_ 2 2 _1_ 2 _1_ 2 4 ___ [ 4 x y + 16 x + 64 + 16 x 4 x y 8 xy ; 4 x y + 16 x + 64 y 4 x y + 8 xy 16 xy] 2 506 _1_ 2 ( 5ab 2 a b) 2 2 2 3 2 2 2 2 2 3 2 2 _1_ 4 _1_ 4 [25a b + 4 a + b + 5a b + 10ab + a b; 25a b + 4 a + b + 5a b 10ab a b] 2 507 508 3 2 _1_ (2a b c c + 2 d) _3_a2b3 ab2 + b (5 509 (an + b + 1)2 358 2 _1_ 2 (5ab + 2 a b) 2 ) 2 3 4 _1_ (abc 2 ab 2c ) 6 4 2 2 3 2 2 3 2 2 2 6 8 2 2 3 4 7 _1_ 2 _1_ 2 2 [4a b c + c + 4 d cd 4a b c + 2a b cd; a b c + 4 a b + 4c a b c + 2abc 4abc ] 2 2 _3_ 2 3 ( 5 a b ab + b) 9 4 6 9 4 6 2 4 2 3 2 4 2 3 ___ _6_ 3 5 _6_ 2 4 ___ _6_ 2 4 _6_ 3 5 [ 25 a b + a b + b 2ab 5 a b + 5 a b ; 25 a b + a b + b 2ab 5 a b + 5 a b ] (an bn + 1)2 con n N [a2n + b2 + 1 + 2anb + 2b + 2an; a2n + b2n + 1 + 2an 2bn 2anbn]