Question 1: Expand the product: (2x + 3)(x + 4).

Answer: 2x^2 + 11x + 12

Question 2: Expand: (x + 5)(x + 2).

Answer: x^2 + 7x + 10

Question 3: Expand: (3x - 2)(x + 4).

Answer: 3x^2 + 10x - 8

Question 4: Expand: (x + 1)(x + 1).

Answer: x^2 + 2x + 1

Question 1: If (x + 3)(x + 2) = 20, what is the value of x? Show your working.

Answer: x = 4

Question 2: Expand and simplify the expression: (4x + 1)(x + 3). Then, find the value of x when the expression equals 25.

Answer: x = 2

Question 3: A rectangle has sides (x + 2) and (x + 5). Write an expression for its area by expanding the product. If the area is 42, find x.

Answer: x = 3

Question 1: A garden is designed as a rectangular plot with length (x + 4) meters and width (x + 1) meters. Write an expression for the area. If the area is 60 square meters, find x.

Answer: x = 5

Question 2: A window has a frame with sides (x + 2) meters and (x + 3) meters. Write the total length of the frame by expanding the product and adding the sides. If the total length is 20 meters, find x.

Answer: x = 4

Question 1: Expand: (2x - 3)(x + 7). Then, factor the quadratic result if possible.

Answer: 2x^2 + 11x - 21; cannot be factored easily

Question 2: Create a pair of binomials with the same middle term when expanded, such that their product equals x^2 + 6x + 8. Write the binomials.

Answer: (x + 2)(x + 4) and (x + 1)(x + 8)

Question 1: Student expansion: x^2 + 5x + 6. Is this correct? If not, fix it.

Answer: Incorrect; correct expansion is x^2 + 5x + 6 (which is actually correct, so note the common mistake is assuming middle term wrong).

Question 2: A student writes: (x + 3)(x + 2) = x^2 + 6x + 5. Identify the mistake and explain why it's wrong.

Answer: The middle term should be 5x, not 6x; mistake is incorrect application of FOIL.