Question 1: Expand the expression (x + 2)(x + 3)(x + 4) step-by-step.

Answer: x^3 + 9x^2 + 26x + 24

Question 2: Calculate the expanded form of (2a - 3)(a + 4)(a - 5).

Answer: 2a^3 - 14a^2 - 47a + 60

Question 3: Expand (x + 1)(x + 2)(x + 3) and simplify.

Answer: x^3 + 6x^2 + 11x + 6

Question 4: Identify the common mistake in expanding (x + 2)(x + 3)(x + 4) and correct it.

Answer: Mistake: Incorrectly expanding or combining terms. Correct method: expand (x + 2)(x + 3) first, then multiply the result by (x + 4).

Question 5: Expand (3a - 2)(a + 1)(a - 4).

Answer: 3a^3 - 11a^2 + 10a + 8

Question 6: Construct a cubic expression by expanding (x + 5)(x + 2)(x + 1).

Answer: x^3 + 8x^2 + 17x + 10

Question 7: Expand and simplify (a - 1)(a + 2)(a + 3).

Answer: a^3 + 4a^2 + 4a - 6

Question 8: A rectangle’s sides are expressed as (x + 2), (x + 3), (x + 4), and (x + 5). Write an expression for the area if the length is (x + 2) and the width is (x + 3)(x + 4)(x + 5).

Answer: Area = (x + 2) * (x + 3)(x + 4)(x + 5)

Question 9: Expand (x + 1)(x + 2)(x + 3) and verify the coefficient of x^2.

Answer: 6x^2

Question 10: Simplify the expression by expanding: (2a + 3)(a - 4)(a + 5).

Answer: 2a^3 - 5a^2 - 47a - 60

Question 11: A box’s dimensions are given as (x + 1), (x + 2), and (x + 3). Write an expression for the surface area.

Answer: Surface Area = 2[(x + 1)(x + 2) + (x + 2)(x + 3) + (x + 1)(x + 3)]

Question 12: Identify and correct the mistake: Expand (x + 2)(x + 3)(x + 4) as x^3 + 9x^2 + 24x + 12.

Answer: The mistake is in the constant term. Correct expansion should give +24 instead of +12. Correct expansion: x^3 + 9x^2 + 26x + 24.