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

Answer: x^2 + 8x + 15

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

Answer: x^2 + 2x - 8

Question 3: Calculate (x + 1)(x + 7) and write the expanded form.

Answer: x^2 + 8x + 7

Question 4: Expand (x + a)(x + b) in terms of a and b.

Answer: x^2 + (a + b)x + ab

Question 5: Expand: (x + 6)(x - 3).

Answer: x^2 + 3x - 18

Question 6: Identify and correct the mistake: (x + 2)(x + 4) = x^2 + 6x + 8.

Answer: Incorrect; correct expansion is x^2 + 6x + 8, so the initial expansion is actually correct. But if the student wrote x^2 + 6x + 8, they are correct. If they wrote something else, fix it accordingly.

Question 7: Express (x + a)(x + b) as a quadratic in x.

Answer: x^2 + (a + b)x + ab

Question 8: If (x + p)(x + q) = x^2 + 5x + 6, find p and q.

Answer: p=2, q=3 (or p=3, q=2)

Question 9: Construct a quadratic expression by expanding (x + 4)(x - 1).

Answer: x^2 + 3x - 4

Question 10: Expand: (x + a)(x + b) and identify the coefficient of x.

Answer: a + b

Question 11: A rectangle's length is modeled by (x + 2), and its width by (x + 5). Write an expression for its area and expand it.

Answer: x^2 + 7x + 10

Question 12: Find the expansion of (x + 3)(x + 3).

Answer: x^2 + 6x + 9