6. Раскройте скобки. 1) (p + q)(p² - pq + q²) 2) (k - m)(k² + km + m²) 3) (a + 8)(a² - 8a + 64) 4) (8 - b)(64 + 8b + b²) 5) (c + 6)(c² - 6c + 36) 6) (7 - d)(49 + 7d + d²) 7) (2 + k)(4 - 2k + k²) 8) (1 - t)(1 + t + t²) 9) (m² + n)(m³ - m²n + n²) 10) (x - y³)(x² + xy³ + y⁶) 11) (8a² + b²)(64a⁴ - 8a²b² + b⁴) 12) (2c³ - 3p²)(4c⁶ + 6c³p² + 9p⁴) 13) (4p + 3q³)(16p² - 12pq³ + 9q⁶) 14) (5x² - 6m³)(25x⁴ + 30x²m³ + 36m⁶) 15) (7d³ + 1)(49d⁶ - 7d³ + 1)

6. Раскройте скобки:

1. \[ (p + q)(p^2 - pq + q^2) = p^3 + q^3 \]
2. \[ (k - m)(k^2 + km + m^2) = k^3 - m^3 \]
3. \[ (a + 8)(a^2 - 8a + 64) = a^3 + 8^3 = a^3 + 512 \]
4. \[ (8 - b)(64 + 8b + b^2) = 8^3 - b^3 = 512 - b^3 \]
5. \[ (c + 6)(c^2 - 6c + 36) = c^3 + 6^3 = c^3 + 216 \]
6. \[ (7 - d)(49 + 7d + d^2) = 7^3 - d^3 = 343 - d^3 \]
7. \[ (2 + k)(4 - 2k + k^2) = 2^3 + k^3 = 8 + k^3 \]
8. \[ (1 - t)(1 + t + t^2) = 1^3 - t^3 = 1 - t^3 \]
9. \[ (m^2 + n)(m^3 - m^2n + n^2) \] - Это выражение не соответствует формуле суммы или разности кубов.
10. \[ (x - y^3)(x^2 + xy^3 + y^6) = x^3 - (y^3)^2 = x^3 - y^6 \]
11. \[ (8a^2 + b^2)(64a^4 - 8a^2b^2 + b^4) = (2a)^3^2 + (b^2)^3 = (8a^2)^3 + (b^2)^3 = 512a^6 + b^6 \]
12. \[ (2c^3 - 3p^2)(4c^6 + 6c^3p^2 + 9p^4) = (2c^3)^3 - (3p^2)^3 = 8c^9 - 27p^6 \]
13. \[ (4p + 3q^3)(16p^2 - 12pq^3 + 9q^6) = (4p)^3 + (3q^3)^3 = 64p^3 + 27q^9 \]
14. \[ (5x^2 - 6m^3)(25x^4 + 30x^2m^3 + 36m^6) = (5x^2)^3 - (6m^3)^3 = 125x^6 - 216m^9 \]
15. \[ (7d^3 + 1)(49d^6 - 7d^3 + 1) = (7d^3)^3 + 1^3 = 343d^9 + 1 \]