Question 1: Expand the expression (3x + 2)(x + 5) and simplify your answer.

Answer: 3x^2 + 17x + 10

Question 2: Calculate the expansion of (2x - 4)(x + 3).

Answer: 2x^2 + 2x - 12

Question 3: Construct the expansion of (7x + 1)(2x - 3).

Answer: 14x^2 - 21x + 2x - 3 = 14x^2 - 19x - 3

Question 4: Simplify (x + 4)(x + 4).

Answer: x^2 + 8x + 16

Question 5: Expand and simplify (5x - 2)(3x + 4).

Answer: 15x^2 + 20x - 6x - 8 = 15x^2 + 14x - 8

Question 6: In a rectangular garden, the length is (x+3) meters and the width is (2x - 1) meters. Find the area of the garden in terms of x.

Answer: Area = (x+3)(2x-1) = 2x^2 + 6x - x - 3 = 2x^2 + 5x - 3

Question 7: A student expands (4x + 1)(x - 2). Show the expansion and identify the coefficient of x.

Answer: 4x^2 - 8x + x - 2 = 4x^2 - 7x - 2; coefficient of x is -7

Question 8: Identify and correct the mistake in expanding (x + 3)(x + 4) as x^2 + 12.

Answer: Incorrect expansion: (x + 3)(x + 4) = x^2 + 4x + 3x + 12 = x^2 + 7x + 12

Question 9: Expand (2x - 5)(3x + 2) and check your work by multiplying out.

Answer: 6x^2 + 4x - 15x -10 = 6x^2 - 11x - 10

Question 10: A rectangle's length is (x + 2) meters and width is (x - 1) meters. Write an algebraic expression for the perimeter.

Answer: Perimeter = 2(length + width) = 2[(x + 2) + (x - 1)] = 2(2x + 1) = 4x + 2

Question 11: Challenge: Expand and simplify (x + 3)(x^2 - x + 4).

Answer: x(x^2 - x + 4) + 3(x^2 - x + 4) = x^3 - x^2 + 4x + 3x^2 - 3x + 12 = x^3 + 2x^2 + x + 12