The problem asks: "¿Con qué expresiones podría construirlo? ¿Por qué?" (Which expressions could Geronimo use to construct it, and why?)

The key here is that Geronimo wants to build a square. The expression that would represent the area of a square must be a perfect square trinomial.

Let's analyze the given expressions to identify any perfect square trinomials:

1. a. $9w^2 + 6wz + z^2$
   This can be rewritten as $(3w + z)^2$, which is a perfect square trinomial.

2. b. $25x^2 - 60xy + 36y^2$
   This is also a perfect square trinomial, as it can be rewritten as $(5x - 6y)^2$.

3. c. $25x^2 - 35xy + 49y^2$
   This is not a perfect square trinomial. The middle term does not match the pattern required for a perfect square trinomial.

4. d. $9x^2 - 12yx + 4y^2$
   This is a perfect square trinomial because it can be rewritten as $(3x - 2y)^2$.

Conclusion:

Geronimo could use expressions a, b, and d to construct the square because they represent perfect square trinomials. Expression c does not form a perfect square, so it cannot be used.

Would you like to know more details about perfect square trinomials or how to recognize them?

Here are five follow-up questions to further expand your understanding:

1. What makes a trinomial a perfect square trinomial?
2. How can you factor other types of quadratic trinomials?
3. Why is the middle term critical in recognizing a perfect square trinomial?
4. Can a square have more than one possible algebraic expression for its area?
5. What are some common mistakes when identifying perfect square trinomials?

Tip: When looking for perfect square trinomials, check if the first and last terms are squares and if the middle term is twice the product of their square roots!