20.14. Представьте в виде произведения выражение: 1) (m² - 2m)² - 1; 2) 16 - (m² + 4m)²; 3) x² - 18xy + 81y² - z²; 4) c² + 4c + 4 - k²; 5) c² - a² + 22a – 121; 6) 100 - 25y² – 60x²y - 36x⁴. 20.15. Разложите на множители: 1) a²-b² - a - b; 2) x - y - x² + y²; 3) 4m² - 9n² + 2m + 3n; 4) c² - d² + 4c - 4d; 5) 5x²у - 5xy² – x² + y²; 6) a² - 10a + 25 - ab + 5b; 7) 8mp + 8np - m² - 2mn – n²; 8) a³ + b³ - a²b - ab²; 9) m³ - 8n³ - m² + 4mn - 4n²; 10) a³ - 4a² + 4a - 1.

20.14

1. \[ (m^2 - 2m)^2 - 1 = (m^2 - 2m - 1)(m^2 - 2m + 1) = (m^2 - 2m - 1)(m - 1)^2 \]
2. \[ 16 - (m^2 + 4m)^2 = (4 - (m^2 + 4m))(4 + (m^2 + 4m)) = (4 - m^2 - 4m)(4 + m^2 + 4m) = -(m^2 + 4m - 4)(m^2 + 4m + 4) = -(m^2 + 4m - 4)(m + 2)^2 \]
3. \[ x^2 - 18xy + 81y^2 - z^2 = (x - 9y)^2 - z^2 = (x - 9y - z)(x - 9y + z) \]
4. \[ c^2 + 4c + 4 - k^2 = (c + 2)^2 - k^2 = (c + 2 - k)(c + 2 + k) \]
5. \[ c^2 - a^2 + 22a - 121 = c^2 - (a^2 - 22a + 121) = c^2 - (a - 11)^2 = (c - (a - 11))(c + (a - 11)) = (c - a + 11)(c + a - 11) \]
6. \[ 100 - 25y^2 - 60x^2y - 36x^4 = 100 - (25y^2 + 60x^2y + 36x^4) = 100 - (5y + 6x^2)^2 = (10 - (5y + 6x^2))(10 + (5y + 6x^2)) = (10 - 5y - 6x^2)(10 + 5y + 6x^2) \]

20.15

1. \[ a^2 - b^2 - a - b = (a - b)(a + b) - (a + b) = (a + b)(a - b - 1) \]
2. \[ x - y - x^2 + y^2 = (x - y) - (x^2 - y^2) = (x - y) - (x - y)(x + y) = (x - y)(1 - (x + y)) = (x - y)(1 - x - y) \]
3. \[ 4m^2 - 9n^2 + 2m + 3n = (2m - 3n)(2m + 3n) + (2m + 3n) = (2m + 3n)(2m - 3n + 1) \]
4. \[ c^2 - d^2 + 4c - 4d = (c - d)(c + d) + 4(c - d) = (c - d)(c + d + 4) \]
5. \[ 5x^2y - 5xy^2 - x^2 + y^2 = 5xy(x - y) - (x^2 - y^2) = 5xy(x - y) - (x - y)(x + y) = (x - y)(5xy - (x + y)) = (x - y)(5xy - x - y) \]
6. \[ a^2 - 10a + 25 - ab + 5b = (a - 5)^2 - b(a - 5) = (a - 5)(a - 5 - b) \]
7. \[ 8mp + 8np - m^2 - 2mn - n^2 = 8p(m + n) - (m + n)^2 = (m + n)(8p - (m + n)) = (m + n)(8p - m - n) \]
8. \[ a^3 + b^3 - a^2b - ab^2 = (a + b)(a^2 - ab + b^2) - ab(a + b) = (a + b)(a^2 - ab + b^2 - ab) = (a + b)(a^2 - 2ab + b^2) = (a + b)(a - b)^2 \]
9. \[ m^3 - 8n^3 - m^2 + 4mn - 4n^2 = (m - 2n)(m^2 + 2mn + 4n^2) - (m^2 - 4mn + 4n^2) = (m - 2n)(m^2 + 2mn + 4n^2) - (m - 2n)^2 = (m - 2n)(m^2 + 2mn + 4n^2 - (m - 2n)) = (m - 2n)(m^2 + 2mn + 4n^2 - m + 2n) \]
10. \[ a^3 - 4a^2 + 4a - 1 = a^3 - 1 - 4a(a - 1) = (a - 1)(a^2 + a + 1) - 4a(a - 1) = (a - 1)(a^2 + a + 1 - 4a) = (a - 1)(a^2 - 3a + 1) \]

Ответ: Решения выше.

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