Question 1: Expand the expression (2x + 3)(x + 4) and simplify your answer.

Answer: 2x^2 + 11x + 12

Question 2: Calculate the expansion of (5x - 2)(3x + 7).

Answer: 15x^2 + 31x - 14

Question 3: Expand (x + 5)(x + 2).

Answer: x^2 + 7x + 10

Question 4: Using the formula (ax + b)(cx + d), expand (3x - 4)(2x + 5).

Answer: 6x^2 + 7x - 20

Question 5: Expand and simplify: (x - 1)(x + 3).

Answer: x^2 + 2x - 3

Question 6: Calculate the expansion of (4x + 1)(x - 2).

Answer: 4x^2 - 7x - 2

Question 7: Expand (7x + 2)(3x - 5).

Answer: 21x^2 - 29x - 10

Question 8: Construct the expansion of (ax + b)(cx + d) when a=2, b=3, c=4, d=5. Write out the general form.

Answer: 2c x^2 + (2d + 3c) x + 15

Question 9: If (ax + b)(cx + d) expands to 6x^2 + 11x + 10, find possible values of a, b, c, d assuming integer coefficients.

Answer: a=2, c=3, b=1, d=5 (or other valid combinations satisfying the expansion)

Question 10: Identify and correct the mistake in expanding (3x + 2)(x + 4) to get 3x^2 + 14x + 8.

Answer: Incorrect expansion; correct is 3x^2 + 14x + 8 (no mistake in this case, but prompt for common mistakes)

Question 11: For the expression (ax + b)(cx + d), if the expanded form is 4x^2 + 7x + 10, find possible values of a, b, c, d.

Answer: a=2, c=2, b=3, d=4 (or other valid sets matching coefficients)

Question 12: Evaluate the expansion of (x + 6)(x + 9).

Answer: x^2 + 15x + 54