Question 1: Factor the expression: x^2 - 9.

Answer: (x + 3)(x - 3)

Question 2: What is the difference of squares for the numbers 64 and 36?

Answer: 8^2 - 6^2

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

Answer: x^2 - 25

Question 4: Identify the pattern in the following sequence: 3^2 - 1^2, 4^2 - 2^2, 5^2 - 3^2, ...

Answer: The pattern is (n+2)^2 - n^2, which simplifies to 4n + 4.

Question 5: Factor the expression: 49 - x^2.

Answer: (7 + x)(7 - x)

Question 6: A rectangular garden has a length of 10 meters plus x, and a width of x. Write an expression for the area, then factor it using a difference of squares if possible.

Answer: Area = x(10 + x) = 10x + x^2; cannot be factored as difference of squares directly.

Question 7: Identify the common mistake: Students often write x^2 - 25 as (x - 5)^2. What is wrong with this?

Answer: It's not a perfect square; (x - 5)^2 = x^2 - 10x + 25, not x^2 - 25.

Question 8: Solve for x: x^2 - 16 = 0.

Answer: x = ±4

Question 9: Which of the following expressions represents a difference of two squares? a) x^2 + 9, b) x^2 - 16, c) 4x + 4.

Answer: b

Question 10: Construct an algebraic expression that represents the pattern: (n+1)^2 - n^2.

Answer: 2n + 1

Question 11: Identify and correct the mistake: Simplify (x + 4)^2 - (x - 4)^2 as 8x.

Answer: Correct. (x+4)^2 - (x-4)^2 = 16x, not 8x.

Question 12: Challenge: Factor completely: 81 - 16x^2.

Answer: (9 + 4x)(9 - 4x)