The image you uploaded contains a set of algebraic problems related to expanding and simplifying expressions. Let's go over the steps for each one of the problems:

1. Expand and simplify. a) $(x + 2)(x + 6)$

   To expand:

   = x^2 + 6x + 2x + 12 = x^2 + 8x + 12$$ b) $$(x + 2)(x - 4)$$ To expand: $$(x + 2)(x - 4) = x(x - 4) + 2(x - 4) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8$$ c) $$(3x + 1)(x - 2)$$ To expand: $$(3x + 1)(x - 2) = 3x(x - 2) + 1(x - 2) = 3x^2 - 6x + x - 2 = 3x^2 - 5x - 2$$ d) $$(x - 2)^2$$ To expand: $$(x - 2)^2 = (x - 2)(x - 2) = x(x - 2) - 2(x - 2) = x^2 - 2x - 2x + 4 = x^2 - 4x + 4$$

2. Write a simplified expression for the area of the figure. The figure might represent a rectangle or another geometric shape. Without seeing the actual figure, I can't provide the exact expression. Could you describe it for me? This will help me give you a more accurate solution.

Let me know if you'd like further clarification or details on any of these steps!

Here are 5 follow-up questions to explore the topic further:

1. What are the key strategies to solve more complex algebraic expansions?
2. How do the distributive property and FOIL method help in expanding binomials?
3. Could you explain how factoring is related to expanding expressions?
4. What are some real-world applications of expanding and simplifying algebraic expressions?
5. How do you simplify complex algebraic expressions involving multiple terms?

Tip: Always double-check each step when expanding binomials, and ensure you combine like terms carefully to avoid mistakes.