III. Сумма и разность кубов. a³+b³ = (a + b)(a² + ab + b²) 5. Разложите на множители. 1) x3 + y3 2) m³ - n³ 3) a³ + 8 4) b3 - 27 5) 64 + c3 6) 125 - d³ 7) m³ + 216 8) 343 + n³ 9) 8x3 1 10) 1 + 1000y3 11) 16a3-27c3 12) 343b3 + 8d3 |13) 64x6 - 125m³ 14) 729n12 + 1 15) 8y³ + 512z9

Ответ: смотри решение

1. \[x^3 + y^3 = (x+y)(x^2 - xy + y^2)\]
2. \[m^3 - n^3 = (m-n)(m^2 + mn + n^2)\]
3. \[a^3 + 8 = a^3 + 2^3 = (a+2)(a^2 - 2a + 4)\]
4. \[b^3 - 27 = b^3 - 3^3 = (b-3)(b^2 + 3b + 9)\]
5. \[64 + c^3 = 4^3 + c^3 = (4+c)(16 - 4c + c^2)\]
6. \[125 - d^3 = 5^3 - d^3 = (5-d)(25 + 5d + d^2)\]
7. \[m^3 + 216 = m^3 + 6^3 = (m+6)(m^2 - 6m + 36)\]
8. \[343 + n^3 = 7^3 + n^3 = (7+n)(49 - 7n + n^2)\]
9. \[8x^3 - 1 = (2x)^3 - 1^3 = (2x-1)(4x^2 + 2x + 1)\]
10. \[1 + 1000y^3 = 1^3 + (10y)^3 = (1+10y)(1 - 10y + 100y^2)\]
11. \[16a^3 - 27c^3 = (2\sqrt[3]{2}a)^3 - (3c)^3 = (2\sqrt[3]{2}a - 3c)(4\sqrt[3]{4}a^2 + 6\sqrt[3]{2}ac + 9c^2)\]
12. \[343b^3 + 8d^3 = (7b)^3 + (2d)^3 = (7b+2d)(49b^2 - 14bd + 4d^2)\]
13. \[64x^6 - 125m^3 = (4x^2)^3 - (5m)^3 = (4x^2-5m)(16x^4 + 20x^2m + 25m^2)\]
14. \[729n^{12} + 1 = (9n^4)^3 + 1^3 = (9n^4+1)(81n^8 - 9n^4 + 1)\]
15. \[8y^3 + 512z^9 = (2y)^3 + (8z^3)^3 = (2y+8z^3)(4y^2 - 16yz^3 + 64z^6)\]

Ответ: смотри решение