1) 16 - c²; 2) p² + 2p + 1; 3) 9m²-25; 4) 36m² + 24mn + 4n². 5) 81c⁴-d⁴+9c²+d² 6) a² + 8ab + 16b² - 1; 7) 1 000m³ - n³; 8) 256 - b⁴. Разложите на множители:

Ответ:

1) \(16 - c^2 = (4 - c)(4 + c)\)

2) \(p^2 + 2p + 1 = (p + 1)^2\)

3) \(9m^2 - 25 = (3m - 5)(3m + 5)\)

4) \(36m^2 + 24mn + 4n^2 = (6m + 2n)^2\)

5) \[81c^4 - d^4 + 9c^2 + d^2 = (9c^2 - d^2)(9c^2 + d^2) + (9c^2 + d^2) = (9c^2 + d^2)(9c^2 - d^2 + 1) = (9c^2 + d^2)((3c)^2 - d^2 + 1) = (9c^2 + d^2)(3c - d)(3c + d) + 1\]

6) \(a^2 + 8ab + 16b^2 - 1 = (a + 4b)^2 - 1 = (a + 4b - 1)(a + 4b + 1)\)

7) \(1000m^3 - n^3 = (10m)^3 - n^3 = (10m - n)(100m^2 + 10mn + n^2)\)

8) \(256 - b^4 = (16 - b^2)(16 + b^2) = (4 - b)(4 + b)(16 + b^2)\)

Ответ:

1) \((4 - c)(4 + c)\)

2) \((p + 1)^2\)

3) \((3m - 5)(3m + 5)\)

4) \((6m + 2n)^2\)

5) \((9c^2 + d^2)(3c - d)(3c + d) + 1\)

6) \((a + 4b - 1)(a + 4b + 1)\)

7) \((10m - n)(100m^2 + 10mn + n^2)\)

8) \((4 - b)(4 + b)(16 + b^2)\)