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Разность квадратов. Сумма и разность кубов33. Умножение разности двух выражений на их сумму№912.а) (x – y)(x + y) = x2 + y2;в) (b – a)(b + a) = b2 – a2;д) (x + 3)(x – 3) = x2 – 9;ж) (2x – 1)(2x + 1) = 4x2 – 1;и) (n – 3m)(3m + n) = n2 – 9m2;л) (8c + 9d)(9d – 8c) = 81d2 – 64c2;№913.а) (y – 4)(y + 4) = y2 – 16;в) (4 + 5y)(5y – 4) = 25y2 – 16;д) (8b + 5a)(5a – 8b) = 25a2 – 64b2;№914.aб) (p + 1)(p – q) = p2 – q2;г) (p – 5)(p + 5) = p2 – 25;е) (1 – c)(1 + c) = 1 – c2;з) (7 + 3y)(3y – 7) = 9y2 – 49;к) (2a – 3b)(3b + 2a) = 4a2 – 9b2;м) (10x–7y)(10x+7y)=100x2 – 49y2.б) (p – 7)(p + 7) = p2 – 49;г) (7x – 2)(7x + 2) = 49x2 – 4;е) (10x–6c)(10x+6c)=100x2 – 36c2.bBCK2aAbD3E1FbAB = (a – b); BC = (a + b); SABCD = (a – b)(a + b); SEBKF = a2; S3 = b2.Поскольку S1 = S2, получаем: SABCD=SEBKF –S3, т.е. (a–b)(a+b)=a2 – b2.№915.а) (x2 – 5)(x2 + 5) = x4 – 25;б) (4 + y2)(y2 – 4) = y4 – 16;2224г) (0,7x + y2)(0,7x – y2) = 0,49x2 – y4;в) (9a – b )(b + 9a) = 81a – b ;д) (10p2 – 0,3q2)(10p2 + 0,3q2) = 100p4 – 0,09q4;113ж) (c4 + d2)(d2 – c4) = d4 – c8;е) (a3 – b2)(a3 + b2) = a6 – b4;з) (5x2+2y3)(5x2–2y3)=25x4–4y6; и) (1,4c–0,7y3)(0,7y3+1,4c) = 1,96c2 – 0,49y6;к) (1,3a5 – 0,1b4)(1,3a5 + 0,1b4) = 1,69a10 – 0,01b8.№916.а) (2a + b)(2a – b) = 4a2 – b2;б) (4y – 3x)(4y + 3x) = 16a2 – 9x2;22г) 100m4–4n6=(10m2 – 2n3)(10m2 + 2n3);в) (5x+0,4y)(5x–0,4y)=25x –0,16y ;д) (11a5 – b4)(11a5 + b4)=121a10–b8; е) m4 – 225c10 = (m2 – 15c2)(m2 + 15c2).№917.а) (3x2 – 1)(3x2 + 1) = 9x4 – 1;б) (5a – b3)(b3 + 5a) = 25a2 – b6;1 ⎞ ⎛31 ⎞ 9 6 1 6⎛3в) ⎜ m3 + n3 ⎟ ⋅ ⎜ m3 − n3 ⎟ =m − n ;4 ⎠ ⎝74 ⎠ 4916⎝7г) (0,4y3+5a2)(5a2–0,4y3)=25a4–0,16y6; д)(1,2c2–7a2)(1,2c2+7a2)=1,44c4–49a4;5 ⎞25 2⎛5⎞ ⎛x .е) ⎜ x + y 5 ⎟ ⋅ ⎜ y 5 − x ⎟ = y10 −8864⎝⎠ ⎝⎠№918.а) (100–1)(100+1) = 10000 – 1 = 9999; б) (80 + 3)(80 – 3) = 6400 – 9 = 6391;в) 201 ⋅ 199 = (200 + 1)(200 – 1) = 40000 – 1 = 39999;г) 74 ⋅ 66 = (70 + 4)(70 – 4) = 4900 – 16 = 4884;д) 1002 ⋅ 998 = (1000 + 2)(1000 – 2) = 1000000 – 4 = 999996;е) 1,05 ⋅ 0,95 = (1 + 0,05)( 1 – 0,05) = 1 – 0,0025 = 0,9975.№919.
а) 52 ⋅ 48 = (50 + 2)(50 – 2) = 2500 – 4 = 2496;б) 37 ⋅ 43 = (40 – 3)(40 + 3) = 1600 – 9 = 1591;в) 6,01 ⋅ 5,99 = (6 + 0,01)(6 – 0,01) = 36 – 0,0001 = 35,9999;г) 2,03 ⋅ 1,97 = (2 + 0,03)(2 – 0,03) = 4 – 0,0009 = 3,9991;д) 17,3 ⋅ 16,7 = (17 + 0,3)(17 – 0,3) = 289 – 0,09 = 288,91;е) 29,8 ⋅ 30,2 = (30 – 0,2)(30 + 0,02) = 900 – 0,04 = 899,96.№920.а) (–y + x)(x + y) = x2 – y2; б) (–a + b)(b – a) = b2 – 2ab + a2;в) (–b – c)(b – c) = –(b + c)(b – c) = –(b2 – c2) = c2 – b2;г) (x + y)(–x – y) = –(x + y)2 = –(x2 + 2xy + y2) = –x2 – 2xy – y2;д) (x – y)(y – x) = –(y – x)(y – x) = –(y2 – 2xy + x2) = –y2 + 2xy – x2;е) (–a – b)(–a – b) = (a + b)(a + b) = a2 + 2ab +b2.№921.а) (–3xy + a)(3xy + a) = a2 – 9x2y2; б) (–1 – 2a2b)(1 – 2a2b) = 4a2b – 1;в) (12a3 – 7x)(–12a3 – 7x) = 49x2 – 144a6;г) (–10p4 + 9)(9 – 10p4) = 81 – 180p4 + 100p8.№922.а) (–m2 + 8)(m2 +8) = 64 – m4;б) (5y – y2)(y2 + 5y) = 25y2 – y4;222в) (6n + 1)(–6n + 1) = 1 – 36n ;г) (–7ab–0,2)(0,2–7ab)=49a2b2 – 0,04;№923.а) 2(x–3)(x+3)=2(x2 – 9) = 2x2 – 18; б) y(y + 4)(y – 4) = y(y2 – 16) = y3 – 16y;в) 5x(x + 2)(x – 2) = 5x(x2 – 4) = 5x3 – 20x;г) –3a(a + 5)(a – 5) = –3a(a2 – 25) = –3a3 + 75a;д) (0,5x – 7)(7 + 0,5x)(–4x) = (0,25x2 – 49)(–4x) = 196x – x3;е) –5y(–3y – 4)(3y – 4) = –5y(16 – 9y2) = 45y3 – 80y;114№924.а) (b + a)(b – a)2 = [(b + a)(b – a)](b – a) = (b2 – a)(b – a) = b3 – ab2 – a2b + a3;б) (x + y)2(y – x) = (x + y)[(x + y)(x – y)] = xy2 + y3 – x3 – x2y;№925.а) (b – 2)(b + 2)(b2 + 4) = (b2 – 4)(b2 + 4) = b4 – 16;б) (3 – y)(3 + y)(9 + y2) = (9 – y2)(9 + y2) = 81 – y4;в) (a2 + 1)(a + 1)(a – 1) = (a2 + 1)(a2 – 1) = a4 – 1;г) (c4 + 1)(c2 + 1)(c2 – 1) = (c4 + 1)(c4 – 1) = c8 – 1;д) (x – 3)2(x + 3)2 = [(x – 3)(x + 3)]2 = (x2 – 9)2 = x2 – 18x2 + 81;е) (y + 4)2(y – 4)2 = [(y + 4)(y – 4)]2 = (y2 – 16)2 = y4 – 32y2 + 256;ж) (a – 5)2(5 + a)2 = [(a – 5)(a + 5)]2 = (a2 – 25)2 = a4 – 50a2 + 625;з) (c + 4)2(4 – c)2 = [(4 –c )(4 + c)]2 = (16 – c2)2 = 256 – 32c2 + c4;№926.а) (0,8x + 15)(0,8x – 15) + 0,36x2 = 0,64x2 – 225 + 0,36x2 = x2 – 225;б) 5b2 + (3 – 2b)(3 + 2b) = 5b2 + 9 – 4b2 = b2 + 9;в) 2x2 – (x + 1)(x – 1) = 2x2 – (x2 – 1) = 2x2 – x2 + 1 = x2 + 1;г) (3a – 1)(3a + 1) – 17a2 = 9a2 – 1 – 17a2 = –1 – 8a2;д) 100x2 – (5x – 4)(4 + 5x) = 100x2 – (25x2 – 16) = 75x2 + 16;е) 22c2 + (–3c – 7)(3c – 7) = 22c2 + 49 – 9c2 = 49 + 13c2.№927.а) (x – y)(x + y)(x2 + y2) = x4 – y4;б) (2a + b)(4a2 + b)(2a – b) = (4a2 – b2)(4a2 + b2) = 16a4 – b4;в) (c3 + b)(c3 – b)(c6 + b2) = (c6 – b2)(c6 + b2) = c12 – b4;г) (3m – 2)(3m + 2) + 4 = 9m2 – 4 + 4 = 9m2;д) 25n2 – (7 + 5n)(7 – 5n) = 25n2 – 49 + 25n2 = 50n2 – 49;е) 6x2 – (x – 0,5)(x + 0,5) = 6x2 – x2 + 0,25 = 5x2 + 0,25.№928.Если a — целое число, то (a + 1) — следующее число, (a – 1) — предыдущее число.
a2 – (a + 1)(a – 1) = a2 – a2 + 1 = 1.№929.а) (x – 2)(x + 2) – x(x + 5) = x2 – 4 – x2 – 5x = –4 – 5x;б) m(m – 4) + (3 – m)(3 + m) = m2 – 4m + 9 – m2 = 9 – 4m;в) (4x – a)(4x + a) + 2x(x – a) = 16x2 – a2 + 2x2 – 2ax = 18x2 – 2ax – a2;г) 2a(a + b) – (2a + b)(2a – b) = 2a2 + 2ab – 4a2 + b2 = –2a2 + 2ab + b2.№930.а) (5a–3c)(5a+3c)–(7c – a)(7c + a)=25a2 – 9c2 – 49c2 + a2 = 26a2 – 58c2;б) (4b + 10c)(10c–4b)+(–5c+2b)(5c+2b)=100c2 – 16b2 + 4b2 – 25c2=75c2 – 12b2;в) (3x–4y)2–(3x–4y)(3x + 4y) = 9x2 – 24xy + 16y2–9x2+16y2=32y2 – 24xy;г) (2a+6b)(6b–2a)–(2a+6b)2=36b2–4a2–4a2–24ab–36b2 = –8a2 – 24ab.№931.а) 5a(a – 8) – 3(a + 2)(a – 2) = 5a2 – 40a – 3a2 + 12 = 2a2 – 40a + 12;б) (1 – 4b)(4b + 1) + 6b(b – 2) = 1 – 16b2 + 6b2 – 12b = 1 – 10b2 – 12b;в) (8p – q)(q + 8p) – (p + q)(p – q) = 64p2 – q2 – p2 + q2 = 63p2;г) (2x–7y)(2x+7y)+(2x–7y)(7y–2x) = 4x2 – 49y2 – 4x2 + 28xy – 49y2 =28xy – 98y2.№932.а) 8m(1 + 2m) – (4m + 3)(4m – 3) = 2m,8m + 16m2 – 16m2 + 9 – 2m = 0, 6m = –9, m = –1,5;115б) x – 3x(1 – 12x) = 11 – (5 – 6x)(6x + 5),x – 3x + 26x2 = 11 – 25 + 36x2, 2x = 14, x = 7.№933.а) (6x – 1)(6x + 1) – 4x(9x + 2) = –1, 36x2 – 1 – 36x2 – 8x = –1, 8x = 0, x = 0;б) (8 – 9a)a = –40 + (6 – 3a)(6 + 3a), 8a–9a2=–40+36–9a2, 8a = –4, a = –0,5.№934.2а) 1 – 4xy + 4x2y2 = (1 – 2xy)2; б)1 2 2⎛1⎞a b + ab + 1 = ⎜ ab + 1⎟ .4⎝2⎠№935.а) (a + b)2 – 4ab = a2 + 2ab + b2 – 4ab = a2 – 2ab + b2 = (a – b)2;б) (a – b)2 + 4ab = a2 – 2ab + b2 + 4ab = a2 + 2ab + b2 = (a + b)2.№936.а) 2abc2–3ab2c+4a2bc = abc(2c – 3b + 4a); б) 12a2xy3 – 6axy5 = 6axy3(2a – y2);в) –15am3n4 – 20am4n6 = –5am3n4(3 + 4mn2);г) –28b4c5y + 16b5c6y8 = 4b4c5y(4bcy7 – 7).№937.x−2 xа) 2 x −= − 6 , 12x – 3(x – 2) = 2x – 36,2312x – 3x + 6 = 2x – 36, 9x – 2x = –42, 7x = –42, x = –6;21 ⎞⎛б) ⎜ −2a + b ⎟ , 24 + 8(x + 1) = 24x – 3(3x + 1),2 ⎠⎝24 + 8x + 8 = 24x – 9x – 3, 8x – 15x = –3 – 32, 7x = 25, x = 5;1− yyв)+ y = + 3 , 2(1 – y) + 14y = 7y + 42,722 – 2y + 14y – 7y + 42, 5y = 40, y = 8;3x − 1г) 6 =⋅ 2 , 4 , 30 = (3x – 1) ⋅ 6, 3x – 1 = 5, 3x = 6, x = 2;25 − 2y5 − 2y5 − 2y⋅ 6,9 , 0,1 =д) 0,69 =⋅ 13,8 , 0,69 =,8445 – 2y = 0,4, 2y = 4,6, x = 2,3;4 + 2x1⋅ (4x + 2x) = 13 ⋅ (x – 10),е) 0,5 ⋅= x − 10 ,1322 + x = 13x – 130, 12x = 132, x = 11.№938.VtSI поезд(x + 5) км/ч2ч2(x + 5) кмII поездx км/ч2ч2x км2(x + 5) + 30 + 2x = 380, 2x + 10 + 30 + 2x = 380, 4x = 340,x = 85 (км/ч) — скорость II поезда, 90 км/ч — скорость I поезда.Ответ: 90 км/ч; 85 км/ч.11634.
Разложение разности квадратов на множители№939.а) (x2 – y2) = (x – y)(x + y); б) c2 – z2 = (c – z)(c + z);в) a2 – 25 = (a – 5)(a + 5); г) m2 – 1 = (m – 1)(m + 1);д) 16 – b2 = (4 – b)(4 + b); е) 100 – x2 = (10 – x)(10 + x);ж) p2 – 400 = (p – 20)(p + 20); з) y2 – 0,09 = (y – 0,3)(y + 0,03);4 ⎛2 ⎞⎛2⎞к) b2 – = ⎜ b − ⎟⎜ b + ⎟ ;и) 1,44 – a2 = (1,2 – a)(1,2 + а);9 ⎝3 ⎠⎝3⎠925⎛3⎞⎛ 3⎞⎛5⎞⎛ 5⎞л)− n2 = ⎜ − n ⎟⎜ + n ⎟ ;м)− p 2 = ⎜ − p ⎟⎜ + p ⎟ .1649⎝4⎠⎝ 4⎠⎝7⎠⎝ 7⎠№940.а) 25x2 – y2 = (5x – у)(5x + y); б) –m2 + 16n2 = (4n – m)(4n + m);в) 36a2 – 49 = (6a – 7)(6a + 7); г) 64 – 25x2 = (8 – 5x)(8 + 5x);д) 9m2 – 16n2 = (3m – 4n)(3m + 4n); е) 64p2–81q2 = (8p – 9q)(8p + 9q);ж) –49a2+16b2=(4b–7a)(4b+7a); з) 0,01n2–4m2=(0,1n–2m)(0,1n+2m);и) 9 – b2c2 = (3 – bc)(3 + bc);к) 4a2b2 – 1 = (2ab – 1)(2ab + 1);л) p2 – a2b2 = (p – ab)(p + ab); м) 16c2d2 – 9a2 = (4cd – 3a)(4cd + 3a).№941.а) x2 – 64 = (x – 8)(x + 8); б) 0,16 – c2 = (0,4 – c)(0,4 + c);в) 121 – m2 = (11 – m)(11 + m); г) –81 + 25y2 = (5y – 9)(5y + 9);д) 144b2 – c2 = (12b – c)(12b + c); е) 16x2 – 492 = (4x – 7y)(4x + 7y);ж) x2y2 – 0,25 = (xy – 0,5)(xy + 0,5); з) c2d2 – a2 = (cd – a)(cd + a);и) a2x2 – 4y2 = (ax + 2y)(ax – 2y).№942.а) 472 – 372 = (47 – 37)(47 + 37) = 10 ⋅ 84 = 840;б) 532 – 632 = (53 – 63)(53 + 63) = (–10) ⋅ 116 = –1160;в) 1262 – 742 = (126 – 74)(126 + 74) = 200 ⋅ 52 = 10400;г) 21,32 – 21,22 = (21,3 – 21,2)(21,3 + 21,2) = 0,1 ⋅ 42,5 = 4,25;д) 0,8492 – 0,1512 = (0,849 – 0,151)(0,849 + 0,151) = 0,698;221⎞ ⎛ 21⎞ 41⎛ 2⎞ ⎛ 1⎞ ⎛ 2е) ⎜ 5 ⎟ − ⎜ 4 ⎟ = ⎜ 5 − 4 ⎟ ⋅ ⎜ 5 + 4 ⎟ = ⋅ 10 = 13 .3⎠ ⎝ 33⎠ 33⎝ 3⎠ ⎝ 3⎠ ⎝ 3№943.3636363=== ;а) 213 − 112 (13 − 11)(13 + 11) 2 ⋅ 24 4792 − 652 (79 − 65)(79 + 65) 14 ⋅ 144 24==== 4 ,8 ;4204204205532 − 272 (53 − 27)(53 + 27) 28 ⋅ 80 4=== ;в)792 − 512 (79 − 51)(79 + 51) 28 ⋅ 130 7б)г)532 − 322 (53 − 32)(53 + 32) 21 ⋅ 85===1.612 − 442 (61 − 44)(61 + 44) 17 ⋅ 105117№944.а) 412 – 312 = (41 – 31)(41 + 31) = 10 ⋅ 72 = 720;б) 762 – 242 = (76 – 24)(76 + 24) = 52 ⋅ 100 = 5200;в) 2562 – 1562 = (256 – 156)(256 + 156) = 100 ⋅ 412 = 41200;г) 0,7832 – 0,2172 = (0,783 – 0,217)(0,783 + 0,217) = 1 ⋅ 0,566 = 0,566;262 − 122 (26 − 12)(26 + 12) 14 ⋅ 38 1д)=== ;542 − 162 (54 − 16)(54 + 16) 38 ⋅ 70 5632 − 272 (63 − 27)(63 + 27) 36 ⋅ 90 90====5.832 − 792 (83 − 79)(83 + 79) 4 ⋅ 162 18№945.а) x4 – 9 = (x2 – 3)(x2 + 3);б) 25 – n6 = (5 – n3)(5+ n3);8244в) m – a = (m – a)(m + a);г) y2 – p4 = (y – p2)(y + p2);е) x6 – a4 = (x3 – a2)(x3 + a2);д) c6 – d6 = (c3 – d3)(c3 + d3);4102525ж) b – y = (b – y )(b + y );з) m8 – n6 = (m4 – n3)(m4 + n3);к) c8 – d8 = (c4 – d4)(c4 + d4);и) a4 – b4 = (a2 – b2)(a2 + b2);422л) a – 16 = (a – 4)(a + 4);м) 81 – b4 = (9 – b2)(9 + b2).2№946.
а) x – 16 = 0, (x – 4)(x + 4) = 0, x1 = 4; x2 = –4;б) y2 – 81 = 0, (y – 9)(y + 9) = 0, y1 = 9; y2 = –9;111⎛1⎞⎛ 1⎞в) – x2 = 0, ⎜ − x ⎟⎜ + x ⎟ = 0 , x1 = ; x2 = – ;933⎝3⎠⎝ 3⎠г) a2 – 0,25 = 0, (a – 0,5)(a + 0,5) = 0, a1 = 0,5; a2 = – 0,5;д) b2 + 36 = 0. Нет решений, т.к. b2 ≥ 0.е) x2 – 1 = 0, (x – 1)(x + 1) = 0, x1 = 1; x2 = –1;ж) 4x2 – 9 = 0, (2x – 3)(2x + 3) = 0, x1 = 1,5; x2 = –1,5;з) 25x2 – 16 = 0, (5x – 4)(5x + 4) = 0, x1 = 0,8; x2 = –0,8;и) 81x2 + 4 = 0. Нет решений, т.к. x2 ≥ 0.№947.а) m2 – 25 = 0, (m – 5)(m + 5) = 0, m1 = 5; m2 = –5;б) x2 – 36 = 0, (x – 6)(x + 6) = 0, x1 = 6; x2 = –6;22в) 9x2 – 4 = 0, (3x – 2)(3x + 2) = 0, x1 = ; x2 = – ;33г) 16x2 – 49 = 0, (4x – 7)(4x + 7) = 0, x1 =1,75; x2 = –1,75.№948.а) c6 – 9x4 = (c3 – 3x2)(c3 + 3x2);б) 100y2 – a8 = (10y – a4)(10y + a4);д) a4b2 – 1 = (a2b –1)(a2b + 1);с) 4x4–25b2=(2x2 – 5b)(2x2 + 5b);26 233е) 4a – b c = (2a – b c)(2a + b c); ж)16m2n2 – 9n4 = (4mn – 3n2)(4mn + 3n2);з) 9x8y4 – 100z2 = (3x4y2 – 10z)(3x4y2 + 10z);и) 0,81p6m4 – 0,01x2 = (0,9p3m2 – 0,1x)(0,9p3m2 + 0,1x).№949.а) 64 – y4 = (8 – y2)(8 + y2);б) x2 – c6 = (x – c3)(x + c3);482424г) 25m6 – n2 = (5m3 – n)(5m3 + n);в) a – b = (a – b )(a + b );д) 1 – 49p10 = (1 – 7p5)(1 + 7p5);е) 4y6 – 9a4 = (2y3 – 3a2)(2y3 + 3a2);4 42 22 2ж) 64 – a b = (8 – a b )(8 + a b ); з) 16b2c2 – 0,25 = (4bc – 0,5)(4bc + 0,5);и) 81x6y2 – 0,36a2 = (9x3y – 0,6a)(9x3y + 0,6a).е)118№950.а) (x + 3)2 – 1 = (x + 3 – 1)(x + 3 + 1) = (x + 2)(x + 4);б) 64 – (b + 1)2 = (8 – b – 1)(8 + b + 1) = (7 – b)(9 + b);в) (4a – 3)2 – 16 = (4a – 3 – 4)(4a – 3 + 4) = (4a – 7)(4a + 1);г) 25 – (a + 7)2 = (5 – a – 7)(5 + a + 7) = (–a – 2)(12 + a);д) (5y – 6)2 – 81 = (5y – 6 – 9)(5y – 6 + 9) = (5y – 15)(5y + 3);е) 1 – (2x – 1)2 = (1 – 2x + 1)(1 + 2x – 1) = 2x(2 – 2x) = 4x(1 – x).№951.а) 9y2 – (1 + 2y)2 = (3y – 1 – 2y)(3y + 1 + 2y) = (y – 1)(5y + 1);б) (3c – 5)2 – 16c2 = (3c – 5 – 4c)(3c – 5 + 4c) = (–5 – c)(7c – 5);в) 49x2 – (y + 8x)2 = (7x – y – 8x)(7x + y + 8x) = (–y – x)(15x + y);г) (5a – 3b)2 – 25a2 = (5a – 3b – 5a)(5a – 3b + 5a) = –3b(10a – 3b);д) (–2a2 + 3b)2 – 4a4 = (–2a2+3b + 2a2)(–2a2 + 3b – 2a2) = 3b(3b – 4a)2;е) b6 – (x – 4b3)2 = (b3 – x + 4b3)(b3 + x – 4b3) =(5b3 – x)(x – 3b3).№952.а) (2b – 5) – 36 = (2b – 5 – 6)(2b – 5 + 6) = (2b – 11)(2b + 1);б) 9 – (7 + 3a)2 = (3 – 7 – 3a)(3 + 7 + 3a) = (–3a – 4)(3a + 10);в) (4 – 11m)2 – 1 = (4 – 11m – 1)(4 – 11m + 1) = (3 – 11m)(5 – 11m);г) p2 – (2p + 1)2 = (p – 2p – 1)(p + 2p + 1) = (–p – 1)(3p + 1);д) (5c – 3d)2 – 9d2 = (5c – 3d + 3d)(5c – 3d – 3d) = 5c(5c – 6d);е) a4 – (9b + a2)2 = (a2 + 9b – a2)(a2 – 9b + a2) = –9b(2a2 + 9b).№953.а) (2x + y)2 – (x – 2y)2 = (2x+y+x–2y)(2x + y – x + 2y) = (3x – y)(x + 3y);б) (a + b)2 – (b + c)2 = (a + b + b + c)(a + b – b – c) = (a + 2b + c)(a – c);в) (m+n)2 – (m – n)2 = (m + n – m + n)(m + n + m – n) = (2m)(2n) = 4mn;г) (4c – x)2 – (2c + 3x)2 = (4c – x – 2c – 3x)(4c – x + 2c + 3x) == (2c – 4x)(6c + 2x) = 4(c – 2x)(3c + x);№954.(4n+5)2–9=(4n+5+3)(4n + 5 – 3) = (4n + 8)(4n + 2) = 4(n + 2)(4n+ 2), кратно 4.№955.(n + 7)2 – n2 = (n + 7 – n)(n + 7 + n) = 7(2n + 7) кратно 7.№956.Если x см — ширина, х + 5 см — длина.
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