Let's solve the problems step by step.

### 39. Factor the following polynomials:
a) \( 3x - 6y \)
**Solution:**
Factor out the common factor \( 3 \):
\[
3(x - 2y)
\]

b) \( \frac{2}{5} x^2 + 5x^3 + \frac{2}{5} y \)
**Solution:**
Factor out \( \frac{1}{5} \):
\[
\frac{1}{5}(2x^2 + 25x^3 + 2y)
\]

c) \( 14x^2 y - 21xy^2 + 28x^2 y^2 \)
**Solution:**
Factor out the common term \( 7xy \):
\[
7xy(2x - 3y + 4xy)
\]

d) \( \frac{2}{5} x(y - 1) - \frac{2}{5} y(y - 1) \)
**Solution:**
Factor out \( \frac{2}{5}(y - 1) \):
\[
\frac{2}{5}(y - 1)(x - y)
\]

### 40. Calculate the value of the expression:
a) \( 15.91,5 + 150.0,85 \)
**Solution:**
Convert to standard form and sum:
\[
15.91 + 150.85 = 166.76
\]

b) \( x(x - 1) - y(1 - x) \) at \( x = 2001 \) and \( y = 1999 \)
**Solution:**
Substitute the values:
\[
2001(2000) - 1999(1 - 2001) = 2002000 + 3998000 = 6000000
\]

### 41. Find \( x \), given:
a) \( 5x(x - 2000) - x + 2000 = 0 \)
**Solution:**
Rearranging gives us:
\[
5x^2 - 10000x - x + 2000 = 0 \implies 5x^2 - 10001x + 2000 = 0
\]
Use the quadratic formula:
\[
x = \frac{10001 \pm \sqrt{(10001)^2 - 4 \cdot 5 \cdot 2000}}{2 \cdot 5}
\]

b) \( x^3 - 13x = 0 \)
**Solution:**
Factor out \( x \):
\[
x(x^2 - 13) = 0 \implies x = 0, \pm \sqrt{13}
\]

### 42. Prove that \( 55^n + 1 - 55^n \) is divisible by 54 (for \( n \) is a natural number)
**Solution:**
Simplifying the expression:
\[
55^n + 1 - 55^n = 1
\]
Since \( 1 \) is not divisible by \( 54 \), we can infer the question had a typo or was misunderstood, but this simplification confirms \( 1 \) is not divisible by \( 54 \), showing a contradiction or a misunderstanding in the theorem.

If further context suggests a different expression, please clarify for further analysis.