№ 417
a 2 − 3a + 1 a 3 − 3a 2 + a – 2a · + a4 – 3a3 + a2 = 9 0,4 = 2a2 (a2 – 3a + 1) – 5a(a3 – 3a2 + a) + a4 – 3a3 + a2 = 2a4 – 6a3 + 2a2 – – 5a4 + 15a3 – 5a2 + a4 – 3a3 + a2 = – 2a4 + 6a3 – 2a2; x+ y 2x − y – 27y · – y(y + 1) = 2x(x +y) – 3y(2x – y) – y2 – y = б) 12x · 6 9 = 2x2 + 2xy – 6xy + 3y2 – y2 – y = 2x2 + 2y – 4xy – y; а) 18a2 ·
c3 − 5c 2 + c c +1 + c4 – 3c = – 10c · 11 5 = 3c3 (c+1) – 2c(c3 – 5c2 + c) + c4 – 3c = = 3c4 + 3c3 – 2c4 + 10c3 – 2c2 + c4 – 3c = 2c4 + 13c3 – 3c;
в) 33c3 ·
p2 + 5 p − 1 p 3 + 0,5 p 2 − p + 2p4 + 10p3 – 2p2 = – 3p · 0,7 0,1 = 40p2 (p2 + 5p – 1) – 30p(p3 + 0,5p2 – p) + 2p4 + 10p3 – 2p2 = = 40p4 + 200p3 – 40p2 – 30p4 – 15p3 + 30p2 + 2p4 + 10p3 – 2p2 = = 12p4 + 195p3 – 12p2. № 418 a = 3x2 + 4x – 8, b = 2x2 – 7x + 12, c = 5x2 + 3x – 27; а) 2(3x2 + 4x – 8) + 3(5x2 + 3x – 27) + 4(2x2 – 7x + 12) = = 6x2 + 8x – 16 + 15x2 + 9x – 81 + 8x2 – 28x + 48 = 29x2 – 11x – 49; б) 7x(3x2+4x–8)–12x + 15x(5x2 + 3x – 27) – 13 = 21x3 + 28x2 – 56x – 12x + + 75x3 + 45x2 – 405x – 13 = 96x3 + 73x2 – 473x – 13; в) 72x(3x2 + 4x – 8) – 4(2x2 – 7x + 12) + 3x(5x2 + 3x – 27) + 4 = = 216x3 + 288x2 – 576x – 8x2 + 28x – 48 +15x3 + 9x2 – 81x + 4 = = 31x3 + 289x2 – 629x – 44; г) 0,1x2 (3x2 + 4x – 8) + 0,5x(5x2 + 3x – 27) – 0,6x3 (2x2 – 7x + 12) – 17= = 0,3x4 + 0,4x3 – 0,8x2 + 2,5x3 + 1,5x2 – 13,5x – 1,2x5 + 4,2x4 – 7,2x3 – – 17 = – 1,2x5 + 4,5x4 – 4,3x3 + 0,7x2 – 13,5x – 17. № 419 x = 3a2 + 4, y =12a – 13, z = a2 – a + 1, r = 5a3, L = 12a2, m = 4a а) 2(3a2 + 4) + 5a3 (12a – 13) – 12a2 (a2 – a + 1) = = 6a2 + 8 + 60a4 – 65a3 – 12a4 + 12a3 – 12a2 = 48a4 – 53a3 – 60a2 + 8; б) 12a2 (3a2 + 4) – 3 · 4a(12a – 13) = 36a4 + 48a2 – 144a2 + 156a = = 36a4 – 96a2 + 156a; в) 5a3 (3a2 + 4) + 12a2 (12a – 13) – 4a(a2 – a + 1) = 15a5 + 20a3 + + 144a3 – 156a2 – 4a3 + 4a2 – 4a = 15a5 + 160a3 – 152a2 – 4a; г) 4a(3a2 + 4) – 12a2 (a2 – a + 1) + 4 · 5a3 (3a2 + 4) – 14 = = 12a3 + 16a – 12a4 + 12a3 – 12a2 + 60a5 + 80a3 – 14 = = 60a5 – 12a4 + 104a3 + 16a – 14. 65
г) 28p2 ·