makarytchev-gdz-7-1-1289-2003 (542427), страница 18
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Тогда(x + 5)2 – x2 = 95, x2 + 10x + 25 – x2 = 95, 10x = 70,x = 7 см — ширина, 12 см — длина. P = 2(7 + 12) = 2 ⋅ 19 = 38 см.Ответ: 38 см.№957.а) 27a3 = (3a)3; б) – m3 = (–2m)3; в) 8b6 = (2b2)3;г) –64p6 = (–4p2)3; д) –27a3x6 = (–3ax2)3; е) 64a6x9 = (4a2x3)3.№958.а) 0,25x2 – 0,6xy + 036y2 = (0,5x – 0,6y)2;б) –a2 + 0,6a – 0,09 = –(a2 – 2a ⋅ 0,3 + (0,3)2) = –(a – 0,3)2;29 442 ⎞⎛3a + a3 + a 2 = ⎜ a 2 + a ⎟ ;1693 ⎠⎝4г) –16m2 – 24mn – 9n2 = –(4m + 3n)2.в)119№959.а) a2 – ac – ab + bc = a(a – c) – b(a – c) = (a – c)(a – b);б) x3 – y3 + xy – x2y2 = x2(x – y2) + y(x – y2) = (x – y2)(x2 + y).№960.xЕсли x км — расстояние, которое пройдет турист, точ — время, которое4xон шел бы со скоростью 4 км/ч;ч — время, которое он двигался бы со5скоростью 5 км/ч, т.е.:1x 1 x 1т.к.
6 мин = ч, то − = +, 5x–10=4x+2, x=12 км весь путь.104 2 5 10Ответ: 12 км.35. Разложение на множители суммы и разности кубов№961.а) x3 + y3 = (x + y)(x2 – xy + y2); б) m3 – n3 = (m – n)(m2 + mn + n2);в) 8 + a3 = (2 + a)(4 – 2a + a2); г) 27 – y3 = (3 – y)(9 + 3y + y2);д) t3 + 1 = (t + 1)(t2 – t + 1);е) 1 – c3 = (1 – c)(1 + c + c2).№962.а) c2 – d2 = (c – d)(c2 + cd + d2); б)p3 + q3 = (p+ q)(p2 – pq + q2);в) x3 – 64 = (x – 4)(x2 + 4x + 16); г) 125 + a3 = (5 + a)(25 – 5a + a2);д) y3 – 1 = (y – 1)(y2 + y + 1);е) 1 + b3 = (1 + b)(1 – b + b2).№963.а) 8x3 – 1 = (2x – 1)(4x2 + 2x + 1);б) 1 + 27y3 = (1 + 3y)(1 – 3y + y2);11 ⎞⎛1 ⎞⎛в) 8 − a3 = ⎜ 2 − a ⎟⎜ 4 + a + a 2 ⎟ ;824 ⎠⎝⎠⎝1⎛1⎞⎛ 1 5⎞г) m3 + 1000 = ⎜ m + 10 ⎟⎜ − m + 100 ⎟ ;64⎝4⎠⎝ 16 2⎠д) 125a3 – 64b3 = (5a – 4b)(25a2 + 20ab + 16b2);1 31 3 ⎛11 ⎞⎛ 111 2⎞е)x +y = ⎜ x + y ⎟⎜ x 2 − xy +y ⎟.27125359525⎝⎠⎝⎠№964.а) 8 –m3 = (2 –m)(4 + 2m + m2);б) c3 + 27 = (c + 3)(c2 – 3c + 9);11 ⎞⎛ 1 ⎞⎛ 1в) 64x3 + 1 = (4x + 1)(16x2 – 4x + 1); г) 1 − p3 = ⎜1 − p ⎟⎜1 + p + p 2 ⎟ ;8224 ⎠⎝⎠⎝11⎛1⎞⎛ 1⎞д) m3–27n3=(m–3n)(m2+3n+9n2); е) a3 + b3 = ⎜ a + b ⎟⎜ a 2 − ab + b2 ⎟ .82⎝2⎠⎝ 4⎠№965.а) c3 + b6 = (c + b2)(c2 – cb2 + b4);б)a6 + b3 = (a2 + b)(a2 – a2b + b2);в) m9 – n3 = (m3 – n)(m6 + m3n + n2); г) p3 + k9 = (p + k3)(p2 + pk3 + k6);д) a6 + b9 = (a2 + b3)(a4 + a2b3 + b6); е) x9 – y9 = (x3 – y3)(x6 + x3y3 + y6).120№966.а) c3 + b6 = (c + b2)(c2 – cb2 + b4);б) a9 – b6 = (a3 b3)(a6 + a3b2 + b4);6242в) x – 8 = (x – 2)(x + 2x + 4);г) 27 + y9 = (3 + y3)(9 – 3y3 + y6).№967.а) –x3 + y3 = (y – x)(y2 + xy + y2);б) –8 – p3 = –(2 + p)(4 – 2p + p2);1 ⎛11⎞⎛ 1 1⎞⎛ 1⎞⎛ 1 1⎞в) –a6 + = ⎜ − a2 ⎟⎜ + a2 + a4 ⎟ ;г) − − b6 = ⎜ − − b2 ⎟⎜ − b2 + b4 ⎟ ;8 ⎝227⎠⎝ 4 2⎠⎝ 3⎠⎝ 9 3⎠е) x6 + y6 = (x2 + y2)(x4 – x2y2 + y4).д) c6 + 1 = (c2 + 1)(c4 – c2 + 1);№968.а) a3b3–1=(ab–1)(a2b2+ab + 1);б) 1 + x3y3 = (1 + xy)(1 – xy + x2y2);в) 8–a3c3=(2–ac)(4+2ac + a2c2);г) m3n3+27=(mn + 3)(m2n2 – 3mn + 9);6 3 324 222е) a3–m3n9=(a–mn3)(a2+amn3 + m2n6).д) x y –c =(x y–c)(x y +cx y+c );№969.а) 3273 + 1733 = (327 + 173)(3272 – 327 ⋅ 173 + 1732) == 500 ⋅ (3272 – 327 ⋅ 173 + 1732) кратно 500;б) 7313 – 6313 = (731 – 631)(7312 + 731 ⋅ 631 + 6312)==100 ⋅ (7312 + 731 ⋅ 631 + 6312) кратно 100.№970.а) 383+373=(38+37)(382–38⋅37+372)=75 ⋅ (382–38 ⋅ 37+372) кратно 75;б) 993–743=(99–74)(992+99⋅74+742)=25 ⋅ (992+99⋅74+742) кратно 25.№971.а) (11с2 + a3 )(–a3 + 11c2) = 121c4 – a6;б) (0,8x + y4)(–0,8x – y4) = –(0,8x + y4)2 = –0,64x2 – 1,6xy4 – y8;в) (0,3c–0,2d)(0,2d–0,3c) = –(0,3c – 0,2d)2 = – 0,09c2 – 0,12cd – 0,04d2;г) (6x3 – 4x)(–6x3 – 4x) = (–4x)2 – (6x3)2 = 16x2 – 36x6.№972.а) x2 + 4 – x2 – 4x – 4 ≠ 0 для любого x;б) (x – 2)(x + 2) – 4 + x2 = x2 – 4 – 4 + x2 = 2x2 – 8 ≠ 0 для любого x.№973.а) (2x–3)2–2x(4+2x)=11, 4x2–12x+9–8x–4x2 = 11, 20x = –2, x = –0,1;б) (4x–3)(3+4x)–2x(8x–1)=0, 16x2–9–16x2+2x = 0, 2x = 9, x = 4,5.§ 14.
Преобразование целых выражений36. Преобразование целого выражения в многочлен№974.2x2y; 4a2 – b(a – 3b);Не целое1x2 − 1; 9x – .28a2, т.к. есть деление на выражение с переменной.a −3№975. а) x3 + 7x2 + 8 + (x2 – 6x + 4)(x – 1) == x3 + 7x2 + 8 + x3 – x2 – 6x2 + 6x + 4x – 4 = 2x3 + 10x + 4;б) (a2 + 7a – 4)(a – 3) – (a3 + 4a2 – 29a + 11) == a3 – 3a2 + 7a2 – 21a – 4a + 12 – a3 – 4a2 + 29a – 11 = 4a + 1.121№976.а) (5x – 2y)(x + y) – 5x2 = 5x2 + 5xy – 2xy – 2y2 – 5x2 = 3xy – 2y2;б) 3a2 + (3a + b)(b – a) = 3a2 + 3ab – 3a2 + b2 – ab = 2ab + b2;в) 2b(7 – b)–(a+2b)(3–b)=14b – 2b2 – 3a + ab – 6b + 2b2 = 8b – 3a + ab;г) (x+6y)(1–4x)–4x(y–x) = x – 4x2 + 6y – 24xy – 4xy + 4x2=x + 6y – 28xy;д) (a + 2b)(4a – 5b) – (3a – b)(b – a) == 4a2 – 5ab + 8ab – 10b2 – 3ab + 3a2 + b2 – ab = 7a2 – 9b2 – ab;е) (4x – 5y)(3y x) + (2x – y)(x – 2y) == 12xy + 4x2 – 15y2 – 5xy + 2x2 – 4xy – xy + 2y2 = 6x2 + 2xy – 13y2.№977.
а) 3(x – 4)(x + 2) + (3x – 1)(5 – x) = 3(x2 – 2x – 8) + 15x – 3x2 – 5 + x == 3x2 – 6x – 24 + 16x – 3x2 – 5 = 10x – 29;б) (b–5)(7–5b)–2(b + 2)(b–6)=7b–5b2–35 + 25b – 2b2 + 8b+24=–7b2 + 40b – 11;в) (c – 7)(4 + 2c) – 6c(1 – 3c) – (9c – 2)(3 – c) == 4c + 2c2 – 28 – 14c – 6c + 18c2 – 27c + 9c2 + 6 – 2c = 29c2 – 45c – 22;г) 5(a + 3)(5 – a) – (a – 8)(1 – a) – 2a(3a – 6) =25a–5a2+75 – 15a + a2 ++8 – 8a – 6a2 + 12a = –10a2 + 13a + 75 + 8 = –10a2 + 13a + 83;д) 4(2a+1)(5a–3)–3(a+2)(a+3)=4(10a2 – 6a + 5a – 3) – 3(a2 + 5a + 6) == 40a2 – 24a + 20a – 12 – 3a2 – 15a – 18 = 37a2 – 19a – 30;е) –2(6–3m)(m+1)+5(m–4)(m–5)=–2(6m+6–3m2–3m)+5(m2 – 9m + 20)== –12m – 12 + 6m2 + 6m + 5m2 – 45m + 100 = 11m2 – 51m + 88.№978.а) 4(m–n)2+4m(m – n) = 4m2 – 8mn + 4n2 + 4m2 – 4mn=8m2–12mn + 4n2;б) 5x(x – y) – 2(y – x)2 = 5x2 – 5xy – 2y2 + 4xy – 2x2 = 3x2 – xy – 2y2;в) (y + 7)2 – 2(y + 10)(y + 4) = y2 + 14y + 49 – 2(y2 + 14 + 40) == y2 + 14y + 49 – 2y2 – 28y – 80 = –y2 – 14y – 31;г) (x – 5)(6 + 4x) – 3(1 – x)2 = 6x + 4x2 – 30 – 20x – 3(1 – 2x + x2) == 6x + 4x2 – 30 – 20x – 3 + 6x – 3x2 = x2 – 8x – 33.№979.
а) (3m – a)(a + 3m) – (2a + m)(3a – m) == 3am + 9m2 – a2 – 3am – 6a2 + 2am – 3am + m2 = 10m2 – am – 7a2;б) (x – 4y)(x + 3y) + (x + 3y)(3y + x) == x2 + 3xy – 4xy – 12y2 + 3xy + x2 – 9y2 – 3xy = 2x2 – xy – 21y2;22⎞ 22⎞1 ⎛⎛в) a(6a+1)(6a–1) – 0,5a ⎜12a 2 + ⎟ = a(36a2 – 1) – a ⎜12a 2 + ⎟ =3⎠ 33⎠2 ⎝3⎝21= 24a3 – a – 6a3 – a = 18a3 – a;33г) 0,2b(10c – 5b) – 4(0,5b + 2c)(2c – 0,5b) = 2bc – b2 – 4(4c2 – 0,25b2) == 2bc – b2 – 16c2 + b2 = 2bc – 16c2.№980.а) a(1–2a)2–(a2–2)(2–a)+4a3(3a–1)=a(1–4a+4a2) – (2a2–a3–4+2a)+12a4 – 4a3 ==a – 4a2 + 4a3 – 2a2 + a3 + 4 – 2a + 12a4 – 4a3 = 12a4 + a3 – 6a2 – a + 4;б) (x2 – 3x)2 – x(5 – x)(x + 5) – 5x(2x3 – 5) = x4 – 6x3 + 9x2 – x(25 – x2) ––10x4 + 25x = –9x4 – 6x3 + 9x2 + 25x – 25x + x3 = –9x4 – 5x3 + 9x2.№981. а) 6x(5x – 24) – 4(3 – 2x)2 = 30x2 – 144x – 4(9 – 12x + 4x2) == 30x2 – 144x – 36 + 48x – 16x2 = 14x2 – 96x – 36;б) 2y(11y – 9) + 0,5(4y – 3)(4y + 3) = 22y2 – 18y + 0,5(16y2 – 9) == 22y2 – 18y + 8y2 – 4,5 = 30y2 – 18y – 4,5;122в) (a – 3b)(a + 3b) + (2a – 3b)2 – 4a(b – a) == a2 – 9b2 + 4a2 – 12ab + 9b2 – 4ab + 4a2 = 9a2 – 16ab;г) (x + 6y)2 – (6y + 5x)(6y – 5x) + x(12y – 6x) == x2 + 12xy + 36y2 – 36y2 + 25x2 + 12xy – 6x2 = 20x2 + 24xy.№982.1 ⎞⎛1⎞11⎞1⎛⎛а) −3 ⎜ x 2 − ⎟⎜ x 2 + ⎟ + 3 x2 ( x 2 − 1 ) − = −3 ⎜ x 4 − ⎟ + 3x4 – 3x2 – =3 ⎠⎝3⎠39⎠3⎝⎝1442 1222= –3x + + 3x – 3x – = –3x , при x = –1,5, –3х ⋅ (–1,5) = 3 ⋅ 2,25= –6,75;33⎛2 2⎞⎛ 2 2⎞б) 0,9x ⋅ ⎜ x − x ⎟⎜ x + x ⎟ − 0 ,6 x 2 ⋅ (2 x 2 − 1) =⎝3⎠⎝ 3⎠=9 ⎛4 22966⎞x ⋅ ⎜ x − x 2 ⎟ – 1,2x5 + 0,6x3 = x5 − x3 − x5 + x3 =10 ⎝ 9510510⎠433⎞⎛4= − x5 − x 3 = − x3 ⋅ ⎜ x 2 + ⎟ ,51010 ⎠⎝53⎞3⎞35⎛4⎛ 32 3 ⎞⎛4= 28 .при x = –2, − x3 ⎜ x 2 + ⎟ = –(–2)3 ⋅ ⎜ ⋅ 4 + ⎟ = 8 ⋅ ⎜ + ⎟ = 8 ⋅10 ⎠1010 ⎠⎝5⎝ 10 10 ⎠⎝5№983.а) (a – 1)(a2 + 1) (a + 1) – (a2 – 1)2 – 2(a2 – 3) == (a2–1)(a2+1)–(a4–2a2+1)–2a2 + 6 = a4 – 1 – a4 + 2a2 – 1 – 2a2 + 6 = 4;б) (a2 – 3)2 – (a – 2)(a4 + 4)(a + 2) – 6(5 – a2) == a4 – 6a2 + 9 – (a2 – 4)(a2 + 4) – 30 + 6a2 = a4 – 21 – a4 + 16 = – 5.№984.а) (y–3)(y2+9)(y+3)–(2y2–y)2 – 19 =(y2 – 9)(y2 + 9)–(4y4 – 4y3+y2) – 19 == y4 – 81 – 4y4 + 4y3 – y2 – 19 = –3y4 + 4y3 – y2 – 100;б) (1 – a)(1 – a2) + (1 + a)(1 + a2) – 2a(1 +a)(a – 1) == 1–a2–a+a3 + 1 + a2 + a + a3 – 2a(a2 – 1) = 2 + 2a3 – 2a3 + 2a = 2 + 2a.№985.а) (a – 3c)(4c + 2a) + 3c(a + 3c) = (2a –c)(3c + 5a) – 8a2:(a–3c)(4c+2a)+3c(a+3c)=4ac+2a2–12c2–6ac + 3ac + 9c2=2a2 + ac – 3c2(2a–c)(3c+5a)–8a2 = 6ac + 10a2 – 3c2 – 5ac – 8a2 = 2a2 + ac – 3c2 верноб) (1 – 2b)(1 – 5b + b2) + (2b – 1)(1 – 6b + b2) = b(1 – 2b):(1 – 2b)(1 – 5b + b2) + (2b – 1)(1 – 6b + b2) =1 – 5b + b2 – 2b + 10b2 ++ 2b – 12b2 + 2b3 – 1 + 6b – b2 = –2b2 + b, b(1 – 2b) = –2b2 + b верно.№986.а) 25y2 – 15ay + 9a2 — нельзя представить;2б)4 2⎛2⎞b – 0,4bc + 0,09с2 = ⎜ b − 0 ,3c ⎟ ;9⎝3⎠21 21 ⎞5 ⎞⎛⎛b = – ⎜ 9a 2 − 15ab + 6 b2 ⎟ = − ⎜ 3a − b ⎟ ;42 ⎠4⎝⎠⎝г) 0,04x4 – 1,2x3 + 0,09х2 — нельзя представить.в) 15ab – 9a2 – 6123№987.а) –20x4y2 – 35x3y3 = –5x3y2(4x + 7y);б) 3a2b2c + 9ab2c3 = 3ab2c(a2 + 3c2).№988.vTSот деревни до ст.15 км/чxч15x кмравныот ст.
до деревни10 км/ч(x + 1) ч10(x + 1) км15x = 10(x + 1), 15x = 10x + 10, 5x = 10, x = 2 (ч) — время, затраченное велосипедистом на путь от деревни до станции.15 ⋅ 2 = 30 км — от деревни до станции.Ответ: 30 км.№989.vtS11чкмиз A в Bx км/чодинаковое22из B в A(x – 1) км/ч3ч53(x – 1) км51 3133= (x – 1),x = x – | ⋅ 10, 5x = 6x – 6,2 5255x = 6 (км/ч) — скорость движения связного из A в B.Ответ: 6 км/ч.37. Применение различных способовдля разложения на множители№990.а) 5x2 – 5y2 = 5(x2 – y2) = 5(x – y)(x + y);б) am2 – an2 = a(m2 – n2) = a(m – n)(m + n);в) 2ax2 – 2ay2 = 2a(x2 – y2) = 2a(x – y)(x + y);г) 9p2 – 9 = 9(p2 – 1) = 9(p – 1)(p + 1);д) 16x2 – 4 = 4(4x2 – 1) = 4(2x – 1)(2x + 1);е) 75 – 27c2 = 3(25 – 9c2) = 3(5 – c)(5 + c);ж) 3xy2 – 27x = 3x(y2 – 9) = 3x(y – 3)(y + 3);з) 100ac2 – 4a = 4a(25c2 – 1) = 4a(5c – 1)(5c + 1);и) 50my2 – 2mx2 = 2m(25y2 – x2) = 2m(5y – x)(5y + x).№991.а) a3 – a = a(a2 – 1) = a(a – 1)(a + 1);б) x2 – x4 = x2(1 –x2) = x2(1 – x)(1 + x);3 5323г) 2x–2x3=2x(1–x2) = 2x(1 – x)(1 + x);в) y –y = y (1–y ) = y (1 – y)(1 + y);24222д) 81x – x = x (81 – x ) = x (9 – x)(9 + x);е) 4y3 – 100y5 = 4y3(1 – 25y2) = 4y3(1 – 5y)(1 + 5y).№992.а) mx2–my2=m(x2–y2)=m(x–y)(x+y);б) ab2–4ac2=a(b2–4c2)=a(b – 2c)(b + 2c);22в) 6a –24 =6(a –4)=6(a – 2)(a + 2);г) 7b2 – 63 = 7(b2 – 9) = 7(b – 3)(b + 3);д) 4b3–b=b(4b2–1)=b(2b – 1)(2b + 1); е) a3 – ac2 = a(a2 – c2) = a(a – c)(a + c).124№993.
a8 – b8 = (a4)2 – 9b4)2 = (a4 – b4)(a4 + b4) = (a2 – b2)(a2+ b2)(a4 + b4) ==(a – b)(a + b)(a2 + b2)(a4 + b4).№994.а) p4 – 16 = (p2 – 4)(p2 + 4) = (p – 2)(p + 2)(p2 + 4);б) x4 – 81 = (x2 – 9)(x2 + 9) = (x – 3)(x + 3)(x2 + 9);в) y8–1=(y4–1)(y4+1)=(y2–1)(y2+1)(y4+1) =(y – 1)(y + 1)(y2 + 1)(y4 + 1);г) a4 – b8 = (a2 – b4)(a2 + b4) = (a – b2)(a + b2)(a2 + b4).№995.а) 3x2 + 6xy + 3y2 = 3(x + y)2 = 3(х + у)(х + у);б) –m2 + 2m – 1 = –(m2 – 2m + 1) = –(m – 1)2 = –(m – 1)(m – 1);в) –4x – 4 – x2 = –(x2 + 4x + 4) = –(x + 2)2 = –(x + 2)(x + 2);г) 6p2+24q2 + 24 pq = 6(p2 + 4pq + 4q2) = 6(p + 2q)2 = 6(p + 2q)(p + 2q);д) 45x + 30ax + 5a2x = 5x(9 + 6ax + a2) = 5x(3 + a)2 = 5x (3 + a)(3 + a);е) 18cx2–24cx+8c = 2c(9x2 – 12x + 4) = 2c(3x – 2)2 = 2c(3x – 2)(3x – 2).№996.а) 4x3 – 4y3 = 4(x3 – y3) = 4(x – y)(x2 + xy + y2);б) 7(a3 + b3) = 7(a + b)(a2 – ab + b2);в) a(m3 – n3) = a(m – n)(m2 + mn + n2);332г) 16x – 2 = 2(8x – 1) = 2(2x – 1)(4x + 2x + 1);д) 1000m + m4 = m(1000 + m3) = m(10 + m)(100 – 10m + m2);е) x5 – x2 = x2(x3 – 1) = x2(x – 1)(x2 + x + 1);ж) y3 + y6 = y3(1 + y3) = y3(1 + y)(1 + y + y2);з) 27m2 – m5 = m2(27 – m3) = m2(3 – m)(9 + 3m + m2);и) 8a4 – 64a = 8a(a3 – 8) = 8a(a – 2)(a2 + 2a + 4).№997.а) (x6–y6)=(x3)2–(y3)2=(x3 – y3)(x3 + y3)=(x–y)(x2+xy+y2)(x+y)(x2–xy – y2);б) x6 – y6 = (x2)3 – (y2)3 = (x2 – y2)(x4 + x2y2 + y4)=(x–y)(x+y)(x4+x2y2+ y2).№998.а) 2m2 – 4m + 2 = 2(m2 – 2m + 1) = 2(m – 1)2 = 2(m – 1)(m – 1);б) 36 + 24x + 4x2 = 4(9 + 6x + x2) = 4(3 +x)2 = 4(x + 3)(x + 3);в) 8a3 – 8b3 = 8(a3 – b3) = 8(a – b)(a2 + ab + b2);г) 9ax3 + 9ay3 = 9a(x3 + y3) = 9a(x + y)(x2 – xy + y2).№999.а) 4xy + 12y – 4x + 12 = 4y(x + 3) – 4(x – 3) = 4(x + 3)(y – 1);б) 60+6ab–30b–12a=30(2–b)–6a(2–b) = (30 – 6a)(2–b)=6(5 – a)(2 – b);в) –abc – 5ac – 4ab – 20a = –ab(c + 4) – 5a(c + 4) == (–ab – 5a)(c + 4)= –a(b + 5)(c + 4);г) a3 + a2b + a2 + ab = a2(a + b) + a(a + b) = a(a + 1)(a + b).№1000.а) 45b+6a–3ab–90=45(b – 2) – 3a(b –2)=(45–3a)(b–2)=3(15 – a)(b – 2);б) –5xy–40y–15x–120=–5x(y+3)–40(y+3)=(–5x–40)(y+3)=–5(x+8)(y+3);в) ac4–c4+ac3–c3=c4(a–1) + c3(a – 1) = (c4 + c3)(a – 1) = c3(c + 1)(a – 1);г) x3–x2y + x2 – xy = x2(x – y) + x(x – y) = (x2 + x)(x – y) = x(x + 1)(x – y).№1001.а) x2 + 2xc + c2 – d2 = (x – c)2 – d2 = (x – c – d)(x – c + d);б) c2 + 2c + 1 – a2 = (c + 1)2 – a2 = (c + 1 – a)(c + 1 + a);в) p2 – x2 + 6x – 9 = p2 – (x – 3)2 = (p – x + 3)(p + x – 3);г) x2 – a2 – 10a – 25 = x2 – (a + 5)2 = (x – a – 5)(x + a + 5).125№1002.а) x2 + 2xy + y2 – m2 = (x + y)2 – m2 = (x + y – m)(x + y + m);б) p2 – a2 – 2ab – b2 = p2 – (a + b)2 = (p – a – b)(p + a + b);в) b2 – c2 – 8b + 16 = (b – 4)2 – c2 = (b – 4 – c)(b – 4 + c);г) 9 – c2 + a2 – 6a = (a – 3)2 – c2 = (a – 3 – c)(a – 3 + c).№1003.
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