Question 1: Expand the expression (3x + 4)(x + 5) using FOIL.

Answer: 3x^2 + 15x + 4x + 20 = 3x^2 + 19x + 20

Question 2: Calculate the expansion of (2x + 7)(x + 3).

Answer: 2x^2 + 6x + 7x + 21 = 2x^2 + 13x + 21

Question 3: A map shows a route with a horizontal distance represented by (x + 2) km and a vertical distance of (3x + 4) km. If the total area of the map segment is represented by the product of these two distances, expand this area expression.

Answer: (x + 2)(3x + 4) = 3x^2 + 4x + 6x + 8 = 3x^2 + 10x + 8

Question 4: A travel planner designs a rectangular park with length (x + 5) meters and width (2x + 3) meters. Write the expression for the total area and expand it.

Answer: (x + 5)(2x + 3) = 2x^2 + 3x + 10x + 15 = 2x^2 + 13x + 15

Question 5: If a map's scale transforms the actual distances, and the scaled horizontal distance is (x + 1) km and the vertical distance is (x + 4) km, find the expanded expression for the area.

Answer: (x + 1)(x + 4) = x^2 + 4x + x + 4 = x^2 + 5x + 4

Question 6: A map route has a length of (2x + 3) km and a width of (x + 2) km. Expand to find the total area.

Answer: (2x + 3)(x + 2) = 2x^2 + 4x + 3x + 6 = 2x^2 + 7x + 6

Question 7: A city map shows a block with dimensions (x + 4) km by (3x + 2) km. Write and expand the area expression.

Answer: (x + 4)(3x + 2) = 3x^2 + 2x + 12x + 8 = 3x^2 + 14x + 8

Question 8: A map shows two adjacent routes: one is (x + 3) km long, and the other is (4x + 1) km long. Find the product of these lengths after expansion.

Answer: (x + 3)(4x + 1) = 4x^2 + x + 12x + 3 = 4x^2 + 13x + 3

Question 9: Identify the common mistake: expanding (x + 2)(x + 5) as x^2 + 7x.

Answer: Incorrect; correct expansion is x^2 + 5x + 2x + 10 = x^2 + 7x + 10

Question 10: Choose the correct expansion: (3x + 2)(x + 4).

Answer: 3x^2 + 14x + 8