33.1. 1) (2 + x)³; 2) (a – 2)3; 3) (5-b)³; 4) (y+3)3; 5) (а – с)³; 6) (c + d)³; 7) (z - t)³; 8) (k + m)³. 33.2. 1) (4x + 1)³; 2) (1 – 3y)³; 3) (5z - 2)3; 4) (4x-3)3; 5) (a + 2x)³; 6) (2y - 3)³; 7) (p - 3q)³; 8) (3n-2m)3. 33.3. 1) (0,2a + 5)³; 2) (4 -0,5b)³; 3) (0,6c-5)³; 3 4) (-2); 5) (+3); 33.4. 1) (4x + 0,1y)³; 4) (0,3b – 10c)³; 2) (0,2a +30b)³; 1 6)2-k 4 3 3)a-7c); 7 2 9 =n+ -m 2 9 5) (0,5x – 2y)³;

33.1

1. \[(2+x)^3 = 2^3 + 3 \cdot 2^2 \cdot x + 3 \cdot 2 \cdot x^2 + x^3 = 8 + 12x + 6x^2 + x^3\]
2. \[(a-2)^3 = a^3 - 3 \cdot a^2 \cdot 2 + 3 \cdot a \cdot 2^2 - 2^3 = a^3 - 6a^2 + 12a - 8\]
3. \[(5-b)^3 = 5^3 - 3 \cdot 5^2 \cdot b + 3 \cdot 5 \cdot b^2 - b^3 = 125 - 75b + 15b^2 - b^3\]
4. \[(y+3)^3 = y^3 + 3 \cdot y^2 \cdot 3 + 3 \cdot y \cdot 3^2 + 3^3 = y^3 + 9y^2 + 27y + 27\]
5. \[(a-c)^3 = a^3 - 3 \cdot a^2 \cdot c + 3 \cdot a \cdot c^2 - c^3 = a^3 - 3a^2c + 3ac^2 - c^3\]
6. \[(c+d)^3 = c^3 + 3 \cdot c^2 \cdot d + 3 \cdot c \cdot d^2 + d^3 = c^3 + 3c^2d + 3cd^2 + d^3\]
7. \[(z-t)^3 = z^3 - 3 \cdot z^2 \cdot t + 3 \cdot z \cdot t^2 - t^3 = z^3 - 3z^2t + 3zt^2 - t^3\]
8. \[(k+m)^3 = k^3 + 3 \cdot k^2 \cdot m + 3 \cdot k \cdot m^2 + m^3 = k^3 + 3k^2m + 3km^2 + m^3\]

33.2

1. \[(4x+1)^3 = (4x)^3 + 3 \cdot (4x)^2 \cdot 1 + 3 \cdot (4x) \cdot 1^2 + 1^3 = 64x^3 + 48x^2 + 12x + 1\]
2. \[(1-3y)^3 = 1^3 - 3 \cdot 1^2 \cdot (3y) + 3 \cdot 1 \cdot (3y)^2 - (3y)^3 = 1 - 9y + 27y^2 - 27y^3\]
3. \[(5z-2)^3 = (5z)^3 - 3 \cdot (5z)^2 \cdot 2 + 3 \cdot (5z) \cdot 2^2 - 2^3 = 125z^3 - 150z^2 + 60z - 8\]
4. \[(4x-3)^3 = (4x)^3 - 3 \cdot (4x)^2 \cdot 3 + 3 \cdot (4x) \cdot 3^2 - 3^3 = 64x^3 - 144x^2 + 108x - 27\]
5. \[(a+2x)^3 = a^3 + 3 \cdot a^2 \cdot (2x) + 3 \cdot a \cdot (2x)^2 + (2x)^3 = a^3 + 6a^2x + 12ax^2 + 8x^3\]
6. \[(2y-3)^3 = (2y)^3 - 3 \cdot (2y)^2 \cdot 3 + 3 \cdot (2y) \cdot 3^2 - 3^3 = 8y^3 - 36y^2 + 54y - 27\]
7. \[(p-3q)^3 = p^3 - 3 \cdot p^2 \cdot (3q) + 3 \cdot p \cdot (3q)^2 - (3q)^3 = p^3 - 9p^2q + 27pq^2 - 27q^3\]
8. \[(3n-2m)^3 = (3n)^3 - 3 \cdot (3n)^2 \cdot (2m) + 3 \cdot (3n) \cdot (2m)^2 - (2m)^3 = 27n^3 - 54n^2m + 36nm^2 - 8m^3\]

33.3

1. \[(0.2a+5)^3 = (0.2a)^3 + 3 \cdot (0.2a)^2 \cdot 5 + 3 \cdot (0.2a) \cdot 5^2 + 5^3 = 0.008a^3 + 0.6a^2 + 15a + 125\]
2. \[(4-0.5b)^3 = 4^3 - 3 \cdot 4^2 \cdot (0.5b) + 3 \cdot 4 \cdot (0.5b)^2 - (0.5b)^3 = 64 - 24b + 3b^2 - 0.125b^3\]
3. \[(0.6c-5)^3 = (0.6c)^3 - 3 \cdot (0.6c)^2 \cdot 5 + 3 \cdot (0.6c) \cdot 5^2 - 5^3 = 0.216c^3 - 5.4c^2 + 45c - 125\]
4. \[(\frac{1}{2}d - 2)^3 = (\frac{1}{2}d)^3 - 3 \cdot (\frac{1}{2}d)^2 \cdot 2 + 3 \cdot (\frac{1}{2}d) \cdot 2^2 - 2^3 = \frac{1}{8}d^3 - \frac{3}{2}d^2 + 6d - 8\]
5. \[(\frac{1}{3}t + 3)^3 = (\frac{1}{3}t)^3 + 3 \cdot (\frac{1}{3}t)^2 \cdot 3 + 3 \cdot (\frac{1}{3}t) \cdot 3^2 + 3^3 = \frac{1}{27}t^3 + t^2 + 9t + 27\]
6. \[(2 - \frac{1}{4}k)^3 = 2^3 - 3 \cdot 2^2 \cdot (\frac{1}{4}k) + 3 \cdot 2 \cdot (\frac{1}{4}k)^2 - (\frac{1}{4}k)^3 = 8 - 3k + \frac{3}{8}k^2 - \frac{1}{64}k^3\]

33.4

1. \[(4x + 0.1y)^3 = (4x)^3 + 3 \cdot (4x)^2 \cdot (0.1y) + 3 \cdot (4x) \cdot (0.1y)^2 + (0.1y)^3 = 64x^3 + 4.8x^2y + 0.12xy^2 + 0.001y^3\]
2. \[(0.2a + 30b)^3 = (0.2a)^3 + 3 \cdot (0.2a)^2 \cdot (30b) + 3 \cdot (0.2a) \cdot (30b)^2 + (30b)^3 = 0.008a^3 + 3.6a^2b + 540ab^2 + 27000b^3\]
3. \[(\frac{1}{7}a - 7c)^3 = (\frac{1}{7}a)^3 - 3 \cdot (\frac{1}{7}a)^2 \cdot (7c) + 3 \cdot (\frac{1}{7}a) \cdot (7c)^2 - (7c)^3 = \frac{1}{343}a^3 - \frac{3}{7}a^2c + 21ac^2 - 343c^3\]
4. \[(0.3b - 10c)^3 = (0.3b)^3 - 3 \cdot (0.3b)^2 \cdot (10c) + 3 \cdot (0.3b) \cdot (10c)^2 - (10c)^3 = 0.027b^3 - 2.7b^2c + 90bc^2 - 1000c^3\]
5. \[(0.5x - 2y)^3 = (0.5x)^3 - 3 \cdot (0.5x)^2 \cdot (2y) + 3 \cdot (0.5x) \cdot (2y)^2 - (2y)^3 = 0.125x^3 - 1.5x^2y + 6xy^2 - 8y^3\]
6. \[(\frac{2}{9}n + \frac{9}{2}m)^3 = (\frac{2}{9}n)^3 + 3 \cdot (\frac{2}{9}n)^2 \cdot (\frac{9}{2}m) + 3 \cdot (\frac{2}{9}n) \cdot (\frac{9}{2}m)^2 + (\frac{9}{2}m)^3 = \frac{8}{729}n^3 + \frac{2}{3}n^2m + \frac{81}{2}nm^2 + \frac{729}{8}m^3\]

Ответ: смотри решение выше

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