Алгебра 7 класс контрольные работы Виленкин ответы – страница 78

а) (а – 2)(а + 2) – 2а(5 – а) = а² – 4 – 10а + 2а² = 3а² – 10а – 4 б) (у – 9)² – 3у(у + 1) = у² – 18у + 81 – 3у² – 3у = –2у² – 21у + 81 в) 3(х – 4)² – 3х² = 3(х² – 8х + 16) – 3х² = 3х² – 24х + 48 – 3х² = –24х + 48

а) 25х – х³ = х(25 – х²) = х(5 – х)(5 + х) б) 2х² – 20ху + 50у² = 2(х² – 10ху + 25у²) = 2(х – 5у)²

(c² – b)² – (c² – 1)(c² + 1) + 2bc² = c⁴ – 2bc² + b² – c⁴ + 1 + 2bc² = b² + 1 при b = –3 b² + 1 = (–3)² + 1 = 9 + 1 = 10

а) (х – 3)² – 25х² = (x – 3 – 5x)(x – 3 + 5x) = (–4x – 3)(6x – 3) = –3(4х + 1)(2х – 1) б) a² – b² – 4b – 4a = (a – b)(a + b) – 4(a + b) = (a + b)(a – b – 4) в) 8 – y⁶ = (2 – y²)(4 + 2y² + y⁴)

(a + b)² – (a – b)² = 4ab a² + 2ab + b² – a² + 2ab – b² = 4ab 4ab = 4ab – верно. Тождество верно, что и требовалось доказать.

а) 4х(2х – 1) – (х – 3)(х + 3) = 8x² – 4x – x² + 9 = 7x² – 4x + 9 б) (p + 3)(p – 11) + (p + 6)² = p² + 3p – 11p – 33 + p² + 12p + 36 = 2p² + 4p + 3 в) 7(a + b)² – 14ab = 7a² + 14ab + 7b² – 14ab = 7a² + 7b²

а) y³ – 49y = y(y² – 49) = y(y – 7)(y + 7) б) –3a² – 6ab – 3b² = –3(a² + 2ab + b²) = –3(a + b)²

(a – 1)²(a + 1) + (a + 1)(a – 1) = (a – 1)(a – 1)(a + 1) + (a + 1)(a – 1) = (a – 1)(a + 1)(a – 1 + 1) = a(a – 1)(a + 1) = a(a² – 1) = a³ – a при a = –3 a³ – a = (–3)³ – (–3) = –27 + 3 = –24

а) (y – 6)² – 9y² = (y – 6 – 3y)(y – 6 + 3y) = (–2y – 6)(4y – 6) = –4(y + 3)(2y – 3) б) c² – d² – c + d = (c – d)(c + d) – (c – d) = (c – d)(c + d – 1) в) x⁹ + 27 = (x³ + 3)(x⁶ – 3x³ + 9)

(х – у)² + (х + у)² = 2(х² + у²) х² – 2ху + у² + х² + 2ху + у² = 2(х² + у²) 2х² + 2у² = 2(х² + у²) 2(х² + у²) = 2(х² + у²) – верно. Тождество верно, что и требовалось доказать.