The question requires factorizing the given expressions. I will solve the ones listed:

1. $x^2 + 2x + 1$: This is a perfect square trinomial. $x^2 + 2x + 1 = (x + 1)^2$

2. $y^2 + 6y + 9$: Another perfect square trinomial. $y^2 + 6y + 9 = (y + 3)^2$

3. $\omega^2 - 10\omega + 25$: Another perfect square trinomial. $\omega^2 - 10\omega + 25 = (\omega - 5)^2$

4. $16x^2 - 56xy + 49y^2$: This is also a perfect square trinomial. $16x^2 - 56xy + 49y^2 = (4x - 7y)^2$

5. $25x^2 + 40xy + 16y^2$: Another perfect square trinomial. $25x^2 + 40xy + 16y^2 = (5x + 4y)^2$

6. $x^2 - 10xy + 25$: Another perfect square trinomial. $x^2 - 10xy + 25 = (x - 5y)^2$

Would you like me to explain any step further? Here are 5 related questions to expand your understanding:

1. How can you identify a perfect square trinomial?
2. What steps would you follow to factorize a polynomial that isn’t a perfect square?
3. What is the general form of a perfect square trinomial?
4. Can you create your own example of a perfect square trinomial and factorize it?
5. What happens if a trinomial cannot be factored into perfect squares?

**