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кратно 14.§ 21. Способ групировки№ 575а) 2x – x2 = x(2 – x); – 3ax + 2x2 = x(2x – 3a);2ax2 – 3a2x = ax(2x – 3a); 4xy – 2x2y = 2xy(2 – x).Ответ: 2x – x2, 4xy – 2x2y; 2x2 – 3ax, 2ax2 – 3a2x.б) ab – 3b2 = b(a – 3b); a2 – 3ab = a(a – 3b);5 + 10x = 5(1 + 2x); a + 2ax = a(1 + 2x).Ответ: ab – 3b2, a2 – 3ab; 5 + 10x, a + 2ax.в) n2 – nm = n(n – m); 6a2 – 9ab = 3a(2a – 3b);mn – n2 = n(m – n); 2ab – 3b2 = b(2a – 3b).Ответ: 6a2 – 9ab, 2ab – 3b2.г) 4x – 8 = 4(x – 2); x2 – 2x = x(x – 2);–5 – 15m = – 5(m + 3); 21mn + 7n = 7n(3m + 1).Ответ: 4x – 8, x2 – 2x.№ 576а) 2by – bz = b(2y – z); 4ax – az = a(4x – z);2ay – az = a(2y – z); 4bx – bz = b(4x – z).Ответ: 2by – bz, 2ay – az; 4ax – az, 4bx – bz.б) 6ax – 3x = 3x(2a – 1); – 2a – 1;3by – 3y = 3y(b – 1); c – cb = c(1 – b).Ответ: таких двучленов нет.в) a3 – 2a2 = a2(a – 2); 4ab – 2a2b = 2ab(2 – a);5ac2 – 10ac = 5ac(c – 2); 3a – 6 = 3(a –2).Ответ: a3 – 2a2, 3a – 6.г) 3mn2 – 6m2n = 3mn(n – 2m); abn – 2abm = ab(n – 2m);a2x3 – 9a2x = a2x(x2 – 9); 9x2 – x4 = x2(9 – x2).Ответ: 3mn2 – 6m2n, abn – 2abm.№ 577а) 3a + 3 – na – n = 3(a + 1) – n(a +1) = (a + 1)(3 – n);б) 6mx – 2m + 9x – 3 = 2m(3x – 1) + 3(3x – 1) = (2m + 3)(3x – 1);в) ax – 3x – 4a + 12 = x(a – 3) – 4(a – 3) =(x – 4)(a – 3);г) 2mx – 3m – 4x + 6 = m(2x – 3) – 2(2x – 3) = (m – 2)(2x – 3).№ 578а) 7kn – 6k +14n – 12 = k(7n – 6) + 2(7n – 6) = (k + 2)(7n – 6);б) 5a2 – 5ax – 7a + 7x = 5a(a – x) – 7(a – x) = (5a – 7)(a – x);93в) 9m2 – 9mn – 5m + 5n = 9m(m – n) – 5(m – n) = (9m – n)(m – n);г) 6a2 – 2ab – 3ac + bc = 2a(3a – b) – c(3a – b) = (2a – c)(3a – b).№ 579а) 7c2 – c – c3 + 7 = c2(7 – c) + 7 – c = (c2 +1)(7 – c);б) x3 + 28 – 14x2 – 2x = x(x2 – 2) – 14(x2 – 2) = (x – 14)(x2 – 2);в) 2b3 – 6 – 4b2 + 3b = 2b2(b – 2) + 3(b – 2) = (2b3 + 3)(b – 2);г) x3 – 6 + 2x – 3x2 = x2(x – 3) + 2(x – 3) = (x2 + 2)(x – 3).№ 580а) 16ab2+5b2c+10c3+32ac2=16a(b2+2c2)+5c(b2+2c2) = (16a + 5c)(b2 + 2c2);б) 18a2+27ab + 14ac + 21bc = 9a(2a + 3b) + 7c(2a + 3b)=(9a+7c)(2a + 3b);в) 20n2 – 35a – 14an + 50n = 10n(2n + 5) – 7a(2n + 5) = (10n – 7a)(2n + 5);г) 2x2yz–15yz–3xz2+10xy2 = xz(2xy – 3z) + 5y(2xy – 3z) = (xz + 5y)(2xy – 3z).№ 581ax – 2a – 3x + 6 = x(a – 3) – 2(a – 3) = (x – 2)(a – 3);а) 4; б) 0; в) – 2,25; г) 0.№ 5822a + b + 2a2 + ab = (2a + b) + a(2a + b) = (2a + b)(a + 1);а) (– 2 + 998)(– 1 + 1) = 0;б) (91 – 3)(45,5 + 1) = 46,5 · 88 = 4092;в) (2 · 7,4 + (– 2))(7,4 + 1) = 12,8 · 8,4 = 107,52;⎛2⎞223 15г) ⎜ −1 + 8 ⎟ (– 0,5 + 1) = 7 · 0,5 =⋅ =3 .3⎠33 26⎝№ 5835ab – 7b + 5a2 – 7a = b(5a – 7) + a(5a – 7) = (a + b)(5a – 7);а) (0,2+1)(1 – 7) = 1,2 · (– 6) = – 7,2; б) (2,5–0,5)(12,5 – 7) = 2 · 5,5 = 11;в) (3,7 – 3,7)(5 · 3,7 – 7) = 0;г) ((1,4 + 11)(7 – 7) = 0.№ 584а) 40a3b2c + 21bc – 56ac2 – 15a2b3 = 8ac(5a2b2 – 7c) + 3b(7c – 5a2b2) == (8ac – 3b)(5a2b2 – 7c);б) 16xy2–5y2z–10z3+32xz2 = 16x(y2 + 2z2) – 5z(y2 + 2z2)=(16x – 5z)(y2 + 2z2);в) 30x2 + 10c – 25cx – 12x = 5x(6x – 5c) + 2(5c – 6x) = (5x – 2)(6x – 5c);г) 18x2z – 10kxy + 20k2y – 36kxz = 18xz(x – 2k) – 10ky(x – 2k) == (18xz – 10ky)(x – 2k) = 2(9xz – 5ky)(x – 2k).№ 585а) ax2–ay–bx2 + cy + by – cx2 = a(x2–y)–b(x2–y)– c(x2– y)=(x2 – y)(a – b – c);б) xy2–by2 – ax + ab + y2 – a = x(y2 – a) – b(y2 – a)+y2–a=(y2 – a)(x – b + 1);в) ax + bx + cx + ay + by + cy = (x + y)(a + b + c);г) ab – a2b2 + a3b3 – c + abc – ca2b2 == ab(1 – ab +a2b2) – c(1 – ab + a2b2) = (ab – c)(1 – ab + a2b2).94№ 58621a2b – 4b – 12a + 7ab2 = 7ab(3a + b) – 4(b + 3a) = (3a + b)(7ab – 4);262⎛ 14⎞⎛ −14 − 12 ⎞− 4 ⎟ = 1⋅ ⎜= −8 ;⎟=−3333⎝⎠⎝⎠а) (– 1 + 2) ⎜ −⎛⎝1⎞б) ⎜12 + ⎟ ( 4 − 4 ) =0;7⎠1 ⎞⎛ 811⎞⎛8⎞ ⎛8в) ⎜ ⋅ 3 + ⎟⎜ ⋅ 7 ⋅ − 4 ⎟ = ⎜ ⋅ 3 + ⎟ ⋅ (4 – 4) = 0;2 ⎠⎝ 722⎠⎝7⎠ ⎝7⎛ 2⎝ 3⎞⎠г) (– 2 + 3) ⎜ − ⋅ 3 ⋅ 7 − 4 ⎟ = 1 · (– 14 – 4) = – 18.№ 587а) 2,7 · 6,2 – 9,3 · 1,2 + 6,2 · 9,3 – 1,2 · 2,7 == 2,7(6,1 – 1,2) – 9,3(1,2 – 6,2) = (6,2 – 1,2)(2,7 + 9,3) = 12 · 5 = 60;б) 125 · 48 – 31 · 82 – 31 · 43 – 125 · 83 = 125(48 – 83) – 31(82 + 53) == 125(48 – 83 – 31) = 125 · (– 66) = – 8250;в) 14,9 · 1,25 + 0,75 · 1,1 + 14,9 · 0,75 + 1,1 · 25 == 14,9(1,25 + 0,75) + 1,1(25 + 0,75) = 14,9 · 2 + 1,1 · 25,72 == 29,8 + 28,325 = 58,125;1 121 43 533 511= 3 ⋅ 7 + 3 ⋅ 7 = 7 ⋅ 4 = 28 .3323г) 3 ⋅ 4 + 4, 2 ⋅ + 3 ⋅ 2 + 2,8 ⋅ =21 14( 2,8 + 4, 2 ) + 3 ⎛⎜ 4 + 2 ⎞⎟ =33⎝ 55⎠№ 588а) 109 · 9,17 – 5,37 · 72 – 37 · 9,17 + 1,2 · 72 == 9,17(109 – 37) – 72(5,37 – 1,2) = 9,17 · 72 – 72 · 4,17 = 72 · 5 = 360; б)19,9 · 18 – 19,9 · 16 + 30,1 · 18 – 30,1 · 16 == (19,9 + 30,1)(18 – 16) = 50 · 2 = 100;в) 15,5 · 20,8 + 51,5 · 9,2 – 3,5 · 20,8 – 3,5 · 9,2 == 15,5(20,8 + 9,2) – 3,5(20,8 + 9,2) = 30 · 12 = 360;г) 77,3 · 13 + 8 · 37,3 – 77,3 · 8 – 13 · 37,3 == 13(77,3 – 37,3) + 8(37,3 – 77,3) = 40 · 5 = 200.№ 589а) x2 + 6x + 8 = x2 + 2x + 4x + 8 = x(x + 2) + 4(x + 2) = (x + 4)(x + 2);б) x2 – 8x + 15 = x2 – 3x – 5x + 15 = x(x – 3) – 5(x – 3) = (x – 5)(x – 3);в) x2 + 3x + 2 = x2 + x + 2x + 2 = x(x + 1) + 2(x + 1) = (x + 2)(x + 1);г) x2 – 5x + 6 = x2 – 2x – 3x + 6 = x(x – 2) – 3(x – 2) = (x – 2)(x – 3).№ 590а) a2 – 7a + 6 = a2 – a – 6a + 6 = a(a – 1) – 6(a – 1) = (a – 6)(a – 1);б) b2 + 9b – 10 = b2 – b + 10b – 10 = b(b – 1) + 10(b – 1) = (b – 1)(b + 10);95в) y2 – 10y + 24 = y2 – 4y – 6y + 24 = y(y – 4) – 6(y – 4) = (y – 6)(y – 4);г) z2 – 18z – 40 = z2 + 2z – 20z – 40 = z(z + 2) – 20(z + 2) = (z – 20)(z + 2).№ 591а) a2 + 8ab – 9b2 = a2 + ab – 9ab – 9b2 = a(a + b) – 9b(a+b)=(a – 9b)(a + b);б) a2 + 16ab + 55b2 = a2 + 5ab + 11ab + 55b2 == a(a + 5b) + 11b(a + 5b) = (a +11b)(a + 5b);в) x2 + 4xy – 12y2 = x2 – 2xy + 6xy – 12y2 == x(x – 2y) + 6y(x – 2y) = (x + 6y)(x – 6y);г) x2 + 16xy + 39y2 = x2 + 13xy + 3xy + 39xy2 == x(x + 3y) + 13y(x + 3y) = (x + 13y)(x + 3y).№ 592а) x – 3x + 2 = 0;x2 – x – 2x + 2 =0;x(x – 2) – (x – 2) =0;(x – 1)(x – 2) =0;x = 1;x = 2.Ответ: 1; 2.в) x2 – 6x + 8 =0;x2 – 2x – 4x + 8 =0;(x – 2)(x – 4) = 0;x = 2;x = 4.Ответ: 2; 4.б) x2 + 8x + 15 = 0;x2 + 3x + 5x + 15 = 0;x(x + 3) + 5(x + 3) = 0;(x + 3)(x + 5) = 0;x = – 3;x = – 5.Ответ: – 3; – 5.г) x2 – 3x – 4 = 0;x2 + x – 4x – 4 = 0;(x – 4)(x + 1) = 0;x = 4;x = – 1.Ответ: 4; – 1.№ 593а) 2x2 – 5x + 2 = 0;2x2 – 4x – x + 2 = 0;2x(x – 2) – (x – 2) = 0;(2x – 1)(x – 2) = 0;б) 3x2 + 10x + 3 = 0;3x2 + 9x + x + 3 = 0;3x(x + 3) + (x + 3) = 0;(3x + 1)(x + 3) = 0;21; x = 2.21Ответ: ; 2.21; x = – 3.31Ответ: – ; – 3.3x=x=–в) 4x2 + 5x – 6 =0;4x2 + 8x – 3x – 6 = 0;4x(x + 2) – 3(x + 2) = 0;(4x – 3)(x + 2) = 0;г) 3x2 – x – 2 = 0;3x2 – 3x + 2x – 2 = 0;3x(x – 1) + 2(x – 1) = 0;(3x + 2)(x – 1) = 0;3; x = – 2.43Ответ: ; – 2.4x=962; x = 1.32Ответ: – ; 1.3x=–§ 22.
Разложение многочлена на множителис помощью формул сокращенного умножения№ 594а) 4z2 = 2z · 2z = (2z)2; 9b4 = 3b2 · 3b2 = (3b2)2;25m2 = 5m · 5m = (5m)2; 64p2 = 8p · 8p = (8p)2;б) 16a2b4 = (4ab2)2; 81x6y4 = (9x3y2)2;49s2t8 = (7st4)2; 25k2t10 = (5kt5)2;2в)216 2 4 2 ⎛ 4 2 ⎞9 4 12 ⎛ 3 2 6 ⎞p s t = ⎜ ps t ⎟ ;mn = ⎜ m n ⎟ ;25⎝5⎠ 16⎝4⎠224 2 12 ⎛ 2 6 ⎞25 4 8 16 ⎛ 5 2 4 8 ⎞a b = ⎜ ab ⎟ ;xyz = ⎜ x y z ⎟ ;4981⎝9⎠⎝9⎠г) 0,01a4b8 = (0,1a2b4)2; 0,04x6y6 = (0,2x3y3)2;0,49k2L10 = (0,7k4L5)2; 1,21m6n4 = (1,1m3n2)2.№ 595а) 4 – 36a2 = 22 – (6a)2 = (2 – 6a)(2 + 6a);б) 100 – 49b2 = 102 – (7b)2 = (10 – 7b)(10 + 7b);в) 400 – 121c2 = 202 – (11c)2 = (20 – 11c)(20 + 11c);г) 225 – 144d2 = 152 – (12d)2 =(15 – 12d)(15 + 12d).№ 596а) a2 – 9b2 = (a – 3b)(a + 3b);в) m2 – 64n2 = (m – 8n)(m + 8n);б) c2 – 16d2 = (c – 4d)(c + 4d);г) p2 – 100q2 = (p – 10q)(p + 10q).№ 597а) 59x2–121a2=(7x – 11a)(7x + 11a); б) 64p2 – 81q2 = (8p – 9q)(8p + 9q);в) 9m2 – 16n2 = (3m – 4n)(3m + 4n); г) 144y2–81r2 = (12y – 9r)(12y + 9r).№ 598а) x2y2–1=(xy)2–12 = (xy – 1)(xy + 1); б) c2d2–4=(cd)2–22=(cd – 2)(cd + 2);в) m2n2 – 25 = (mn)2 – 52 = (mn – 5)(mn + 5);г) p2q2 – 100 = (pq)2 – 102 = (pq – 10)(pq + 10).№ 599а) 25 – 36p2c2 = 52 – (6pc)2 = (5 – 6pc)(5 + 6pc);б) 100m2n2 – 81 = (10mn)2 – 92 = (10mn – 9)(10mn + 9);в) 49x2y2 – 400 = (7xy)2 – 202 = (7xy – 20)(7xy + 20);г) 225 – 144c2d2 = 152 – (12cd)2 = (15 – 12cd)(15 + 12cd).№ 600а) c2d2 – m2 = (cd)2 – m2 = (cd – m)(cd + m);б) a2x2 – 0,25p2q2 =(ax)2 – (0,5pq)2 = (ax – 0,5pq)(ax + 0,5pq);в) 16y2z2 – 4a2n2 = (4yz)2 – (2an)2 = (4yz – 2an)(4yz + 2an);г) x2y2 – 0,25p2q2 = (xy)2 – (0,5pq)2 = (xy – 0,5pq)(xy + 0,5pq).97№ 601а) 144a4 – 625c2 = (12a2)2 – (25c)2 = (12a2 – 25c)(12a2 + 25c);б) 25p10 –21 ⎞⎛1 ⎞1 12⎛1 ⎞⎛q = (5p5)2 – ⎜ q 6 ⎟ = ⎜ 5 p5 − q 6 ⎟⎜ 5 p5 + q 6 ⎟ ;3 ⎠⎝3 ⎠9⎝3 ⎠⎝в) 169x8 – 400y16 = (13x4 )2 – (20y8)2 = (13x4 – 20y8)(13x4 + 20y8);г) 4b16 –21 ⎞⎛1 ⎞1 4⎛1 ⎞⎛d = (2b8)2 – ⎜ d 2 ⎟ = ⎜ 2b8 − d 2 ⎟⎜ 2b8 − d 2 ⎟ .4 ⎠⎝4 ⎠16⎝4 ⎠⎝№ 602а) x2 – 49 = 0;(x – 7)(x + 7) = 0;x – 7 = 0; x + 7 = 0;x = 7; x = – 7.Ответ: 7; – 7.в) z2 – 625 = 0;(z – 25)(z + 25) = 0;z – 25 = 0; z + 25 = 0;z = 25; z = – 25.Ответ: 25; – 25.б) y2 – 100 = 0;(y – 10)(y + 10) = 0;y – 10 = 0; y + 10 = 0;y = 10; y = – 10.Ответ: 10; – 10.г) t2 – 1 = 0;( t – 1)(t + 1) = 0;t – 1 = 0; t + 1 = 0;t = 1; t = – 1.Ответ: 1; – 1.№ 603а) 4x2 – 1 = 0;(2x – 1)(2x + 1) = 0;2x – 1 = 0; 2x + 1 = 0;б) 25y2 – 49 = 0;(5y – 7)(5y + 7) = 0;5y – 7 = 0; 5y + 7 = 0;11;x=– .221 1Ответ: ;– .2 255;y=– .7755Ответ: ; – .77x=y=в) 26a2 – 25 = 0;(6a – 5)(6a + 5) = 0;6a = 5; 6a = – 5;г) 144z2 – 1 = 0;(12z – 1)(12z + 1) = 0;12z = 1; 12z = – 1;a = 1,2; a = – 1,2.Ответ: 1,2; – 1,2.11;z=–.121211;–.Ответ:1212z=№ 604а) a + b; a2 – ab + b2;в) 2c + 3d; 2c2 – 6cd + 9d2;б) m2 + 2n2; m4 – 2m2n2 + 4n4г) 3p + 4q2; 9p2 – 12pq2 + 16q4.№ 605а) k –L; k2 + kL + L2;в) 3p – 2m; 9p2 + 6pm + 4m2;б) 5a2 – b2; 25a4 + 5a2b2 + b4;г) 4s – 3t2; 16s2 + 125t2 + 9t4.98№ 606а) a3b3 = (ab)3, x6y9 = (x2y3)3, 8m3n9 = (2mn3)3, 125k9t27 = (5k3t9)3;б)1 9 ⎛1p = ⎜64⎝43327 18 ⎛ 3 6 ⎞1⎞⎛1⎞ 125 24 ⎛ 5 8 ⎞p⎟ ,s = ⎜ s ⎟ ;m12 = ⎜ m 4 ⎟ ,a =⎜ a ⎟⎠ 125⎝ 5 ⎠ 343⎝7⎠ 216⎝6 ⎠в) 0,064a3b3 = (0,4ab)3,0,216m3n18 = (0,6mn6)3,г) 125x3y6z9 =(5xy2z3)3,8m6n3p12 = (2m2np4)3,30,125x9y3 = (0,5x3y)3,0,008p9q12 = (0,2p3q4)3;216a12b36c24 = (6a4b12c8)3,0,343k9L18p15 = (0,7k3L6p5)3.№ 607а) a3 + 8 = a3 + 23 = (a + 2)(a2 – 2a + 4);б) b3 – 27 = b3 – 33 = (b – 3)(b2 + 3b + 9);в) c3 – 64 = c3 – 43 = (c – 4)(c2 + 4c + 16);г) d3 + 125 = d3 + 53 = (d + 5)(d2 – 5d + 25).№ 608а) 216 – m3 = 63 – m3 = (6 – m)(36 + 6m + m2);б) 1000 + m3 = 103 + m3 = (10 + m)(100 – 10m + m2);в) 729 + p3 = 93 + p3 = (9 + p)(81 – 9p + p2);г) 343 – q3 = 73 – q3 = (7 – q)(49 + 7q + q2).№ 609а) 64a3 + 1 = (4a + 1)(16a2 – 4a + 1);б) 27d3 – 8=(3d – 2)(9d2 + 6d + 4);в) 512b3 – 125 = (8b – 5)(64b2 + 40b + 25);г) 216c3 + 1000 = (6c + 10)(36c2 – 60c + 100).№ 610а) a3b3–1=(ab – 1)(a2b2 + ab + 1);в) m3n3–27=(mn–3)(m2n2+3mn+9);№ 611а) a2 – 2ab + b2 = (a – b)2;в) z2 + 2zt + t2 = (z + t)2;б) 8 + c3d3 = (2 + cd)(4 – 2cd + c2d2);г) p3q3+64=(pq + 64)(p2q2 – 4pq + 16).б) x2 + 2xy + y2 = (x + y)2;г) m2 – 2mn + n2 = (m – n)2.№ 612а) m2 + 4m + 4 = m2 + 2 · 2m + 22 = (m + 2)2;б) a2 – 12a + 36 = a2 – 2 · 6a + 62 = (a – 6)2;в) 1 – 2b + b2 = (1 – b)2;г) y2 + 18y + 81 = y + 2 · 9y + 92 = (y + 9)2.№ 613а) p2 + 10p + 25 = p2 + 2 · 5p + 52 = (p + 5)2;б) x2 – 14x + 49 = x2 – 2 · 7x + 72 = (x – 7)2;в) 225 – 30y + y2 = 152 – 2 · 15y + y2 = (15 – y)2;г) 64 + 16z + z2 = 82 + 2 · 8z + z2 = (z + 8)2.99№ 614а) 4y2 – 12y + 9 = (2y)2 – 2 · 3 · 2y + 32 = (2y – 3)2;б) 9p2 + 48pq + 64q2 = (3p)2 + 2 · 3p · 8q + (8q)2 = (3p + 8q)2;в) 9m2 + 24m + 16 = (3m)2 + 2 · 4 · 3m + 42 = (3m + 4)2;г) 9a2 – 30a + 25 = (3a)2 – 2 · 5 · 3a + 52 = (3a – 5)2.№ 615а) 9x2 + 24xy + 26y2 = (3x)2 + 2 · 3x · 4y + (4y)2 = (3x + 4y)2;б) 36a2 – 84ab + 49b2 = (6a)2 – 2 · 6a · 7b + (7b)2 = (6a – 7b)2;в) 4m2 – 28mn + 49n2 = (2m)2 – 2 · 2m · 7n + (7n)2 = (2m – 7n)2;г) 0,25x2 + 3xy + 9y2 = (0,5x)2 + 2 · 0,5x · 3y + (3y)2.№ 616а) a2 – 10a + 25 = (a – 5)2 – неотрицательное;б) 49 + 14a + a2 = (a + 7)2 – неотрицательное;в) – a2 – 4a – 4 = – 1 · (a2 + 4a + 4) = – (a + 2)2 – неположительное;г) – a2 – 12a – 36 = – 1 · (a2 + 12a + 36) = – (a + 6)2 – неположительное.№ 617а) 342 + 2 · 34 · 36 + 362 = (34 + 36)2 = 702 = 4900;б) 272 – 2 · 27 · 13 + 132 = (27 – 13)2 = 142 = 196;в) 982 – 2 · 98 · 8 + 82 = (98 – 8)2 = 902 = 8100;г) 76,4 + 13,6 + 2 · 76,4 · 13,6 = (76,4 + 13,6)2 = 902 = 8100.№ 618а) 2572 – 1432 = (257 – 143)(257 + 143) = 114 · 400 = 45600;б) 73,62 – 26,42 = (73,6 – 26,4)(73,6 + 26,4) = 37,2 · 100 = 3720;в) 1652 – 652 = (165 – 65)(165 + 65) = 100 · 230 = 23000;г) 72,52 – 47,52 = (72,5 – 47,5)(72,5 + 47,5) = 25 · 120 = 3000.№ 619а) (x + 1)2 – 25 = (x + 1 – 5)(x + 1 + 5) = (x – 4)(x + 6);б) (y – 2)2 – 4 = (y – 2 – 2)(y – 2 + 2) = y(y – 4);в) (z + 10)2 – 100 = (z + 10 – 10)(z + 10 + 10) = z(z + 20);г) (t – 7)2 – 100 = (t – 7 – 10)(t – 7 + 10)= (t – 17)(t + 3).№ 620а) 49 – (m – 3)2 = (7 – m + 3)(7 + m – 3) = (m + 4)(10 – m);б) 400 – (a + 9)2 = (20 – a – 9)(20 + a + 9) = (11 – a)(29 + a);в) 625 – (n + 12)2 = (25 – n – 12)(25 + n + 12) = (13 – n)(37 + n);г) 121 – (b – 13)2 = (11 – b + 13)(11 + b – 13) = (24 – b)(b – 2).№ 621а) (a+4)2–(b+2)2=(a + 4 – b – 2)(a + 4 + b + 2) = (a – b + 2)(a + b + 6);б) (x–5)2–(y + 8)2 = (x – 5 – y – 8)(x – 5 + y + 8) = (x – y – 13)(x + y +3);в) (m+10)2–(n–12)2 = (m+10–n+12)(m+10+n – 12)=(m – n + 22)(m + n – 2);г) (c–1)2–(d – 23)2 = (c – 1 – d + 23)(c – 1+ d – 23) =(c – d + 22)(c + d – 24).100№ 622а) (3x+1)2–(4x + 3)2 = (3x + 1 – 4x – 3)(3x + 1 + 4x + 3) = – (x + 2)(7x + 4);б) (6y – 7)2–(9y + 4)2=(6y – 7 – 9y – 4)(6y – 7 + 9y +4)=(– 3y – 11)(15y – 3);в) (15z + 4)2 – (3z – 2)2 = (15z + 4 – 3z + 2)(15z + 4 + 3z – 2) == (12z + 6)(18z + 2) = 12(2z + 1)(3z + 2);г) (3t – 9)2 – (8t – 7)2 = (13t – 9 – 8t + 7)(13t – 9 +8t – 7)=(5t – 2)(21t – 16).№ 6231 2 11 ⎞⎛ 11⎞11 11⎛1a −а)= 0; ⎜ a − ⎟⎜ a + ⎟ = 0; a = ; a = − ;5 ⎠⎝ 45⎠162545 45⎝44444; a = − .
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