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

Answer: x^2 + 8x + 15

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

Answer: x^2 + 9x + 14

Question 3: What is the expanded form of (x-4)(x+6)?

Answer: x^2 + 2x - 24

Question 4: Simplify the expression (x+1)(x+1).

Answer: x^2 + 2x + 1

Question 5: Expand and simplify: (x+4)(x+9).

Answer: x^2 + 13x + 36

Question 6: A rectangular garden has a length of (x+2) meters and a width of (x+5) meters. Write an expression for the area of the garden and expand it.

Answer: x^2 + 7x + 10

Question 7: A company designs rectangular banners with sides (x+3) meters and (x+4) meters. Find an expression for the area, expand, and interpret the result.

Answer: x^2 + 7x + 12

Question 8: Expand (x-3)(x+4) and identify the constant term.

Answer: x^2 + x - 12

Question 9: A square has a side length of (x+1) meters. Write and expand an expression for its area.

Answer: x^2 + 2x + 1

Question 10: If (x+5)(x+2) = x^2 + 7x + 10, what are the values of a and b?

Answer: ["a=5, b=2"]

Question 11: Identify and correct the mistake: Expand (x+3)(x-3) and the student writes x^2 + 3x - 3x.

Answer: The correct expansion is x^2 - 9; the mistake is ignoring the difference of squares pattern.

Question 12: Challenge: Expand (2x+3)(x+4) and express your answer.

Answer: 2x^2 + 11x + 12