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

Answer: x^2 + 8x + 15

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

Answer: x^2 + 9x + 14

Question 3: Expand (x + 1)(x + 6) and simplify.

Answer: x^2 + 7x + 6

Question 4: If (x + a)(x + b) = x^2 + (a + b)x + ab, find the expanded form of (x + 4)(x + 9).

Answer: x^2 + 13x + 36

Question 5: Expand (x + 8)(x + 12).

Answer: x^2 + 20x + 96

Question 6: A rectangle has sides of length (x + 3) and (x + 4). Write an expression for its area by expanding the brackets.

Answer: x^2 + 7x + 12

Question 7: Expand (x + 5)(x + 10).

Answer: x^2 + 15x + 50

Question 8: A student expands (x + 2)(x + 3) and gets x^2 + 5x + 6. Identify and correct any mistake in this expansion.

Answer: Correct expansion is x^2 + 5x + 6; no mistake.

Question 9: Expand (x + 6)(x + 8) and then evaluate for x=2.

Answer: x^2 + 14x + 48; when x=2, value = 4 + 28 + 48 = 80

Question 10: Expand (x + 1)(x + 9) and explain each step.

Answer: x^2 + 10x + 9; step 1: multiply x by x and 1; step 2: multiply 1 by x and 9; step 3: sum terms.

Question 11: Construct a pair of brackets (x + a)(x + b) such that the expansion results in x^2 + 14x + 24. Find possible values of a and b.

Answer: a + b = 14; ab = 24; possible pairs: (2, 12), (3, 11), (4, 10), (6, 8).