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) (l – 1) (l² + l + 1) 9) (m² + n) (m⁴ – m²n + n²) 10) (x – y³) (x² + xy³ + y⁶) 11) (8a² + b²) (64a⁴ – 8a²b² + b⁴) 12) (2c³ – 3p²) (4c⁶ + 6c³p² + 9p⁴) 13) (4p⁶ + 3q³) (16p¹² – 12p⁶q³ + 27q⁶) 14) (5x² – 6m³) (25x⁴ + 30x²m³ + 36m⁶) 15) (7d⁵ + 1) (49d¹⁰ – 7d⁵ + 1)

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. \((2 + k)(4 - 2k + k^2) = (2 + k)(2^2 - 2k + k^2) = 2^3 + k^3 = 8 + k^3\)
8. \((l - 1)(l^2 + l + 1) = l^3 - 1\)
9. \((m^2 + n)(m^4 - m^2n + n^2) = (m^2)^3 + n^3 = m^6 + n^3\)
10. \((x - y^3)(x^2 + xy^3 + y^6) = x^3 - (y^3)^3 = x^3 - y^9\)
11. \((8a^2 + b^2)(64a^4 - 8a^2b^2 + b^4) = (8a^2)^3 + (b^2)^3 = 512a^6 + b^6\)
12. \((2c^3 - 3p^2)(4c^6 + 6c^3p^2 + 9p^4) = (2c^3)^3 - (3p^2)^3 = 8c^9 - 27p^6\)
13. \((4p^6 + 3q^3)(16p^{12} - 12p^6q^3 + 27q^6) = (4p^6)^3 + (3q^3)^3 = 64p^{18} + 27q^9\)
14. \((5x^2 - 6m^3)(25x^4 + 30x^2m^3 + 36m^6) = (5x^2)^3 - (6m^3)^3 = 125x^6 - 216m^9\)
15. \((7d^5 + 1)(49d^{10} - 7d^5 + 1) = (7d^5)^3 + 1^3 = 343d^{15} + 1\)

Ответ:

• \(p^3 + q^3\)
• \(k^3 - m^3\)
• \(a^3 + 512\)
• \(512 - b^3\)
• \(c^3 + 216\)
• \(343 - d^3\)
• \(8 + k^3\)
• \(l^3 - 1\)
• \(m^6 + n^3\)
• \(x^3 - y^9\)
• \(512a^6 + b^6\)
• \(8c^9 - 27p^6\)
• \(64p^{18} + 27q^9\)
• \(125x^6 - 216m^9\)
• \(343d^{15} + 1\)