Вопрос:

4. Раскройте скобки. 1) (b - c)(b + c) 2) (k + m)(k - m) 3) (c - 1)(c + 1) 4) (2 + k)(2 - k) 5) (6 - a)(6 + a) 6) (x + 14a)(x - 14a) 7) (5m - 3k)(3k + 5m) 8) (12v - 11u)(11u + 12v) 9) (9p + n²)(n² - 9p) 10) (15a - 2b²)(15a + 2b²) 11) (6h² - 17m²)(6h² + 17m²) 12) (11x² - 7y³)(11x² + 7y³) 13) (8u³ - 5b²)(8u³ + 5b²) 14) (13a³ - 18b³)(13a³ + 18b³) 15) (20p¹⁰ - 19k⁴)(20p¹⁰ + 19k⁴)

Ответ:

4. Раскройте скобки:

  1. \[ (b - c)(b + c) = b^2 - c^2 \]
  2. \[ (k + m)(k - m) = k^2 - m^2 \]
  3. \[ (c - 1)(c + 1) = c^2 - 1 \]
  4. \[ (2 + k)(2 - k) = 4 - k^2 \]
  5. \[ (6 - a)(6 + a) = 36 - a^2 \]
  6. \[ (x + 14a)(x - 14a) = x^2 - (14a)^2 = x^2 - 196a^2 \]
  7. \[ (5m - 3k)(3k + 5m) = (5m - 3k)(5m + 3k) = (5m)^2 - (3k)^2 = 25m^2 - 9k^2 \]
  8. \[ (12v - 11u)(11u + 12v) = (12v - 11u)(12v + 11u) = (12v)^2 - (11u)^2 = 144v^2 - 121u^2 \]
  9. \[ (9p + n^2)(n^2 - 9p) = (n^2 + 9p)(n^2 - 9p) = (n^2)^2 - (9p)^2 = n^4 - 81p^2 \]
  10. \[ (15a - 2b^2)(15a + 2b^2) = (15a)^2 - (2b^2)^2 = 225a^2 - 4b^4 \]
  11. \[ (6h^2 - 17m^2)(6h^2 + 17m^2) = (6h^2)^2 - (17m^2)^2 = 36h^4 - 289m^4 \]
  12. \[ (11x^2 - 7y^3)(11x^2 + 7y^3) = (11x^2)^2 - (7y^3)^2 = 121x^4 - 49y^6 \]
  13. \[ (8u^3 - 5b^2)(8u^3 + 5b^2) = (8u^3)^2 - (5b^2)^2 = 64u^6 - 25b^4 \]
  14. \[ (13a^3 - 18b^3)(13a^3 + 18b^3) = (13a^3)^2 - (18b^3)^2 = 169a^6 - 324b^6 \]
  15. \[ (20p^{10} - 19k^4)(20p^{10} + 19k^4) = (20p^{10})^2 - (19k^4)^2 = 400p^{20} - 361k^8 \]
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