Question 1: Factor the expression a² - 16.

Answer: a² - 16 = (a - 4)(a + 4)

Question 2: Simplify the expression 49 - b².

Answer: (7 - b)(7 + b)

Question 3: Expand the expression (x - 3)(x + 3).

Answer: x² - 9

Question 1: Factor the expression 81 - 25y².

Answer: (9 - 5y)(9 + 5y)

Question 2: Simplify the expression 100 - 36z².

Answer: (10 - 6z)(10 + 6z)

Question 3: Factor the expression a² - 49.

Answer: (a - 7)(a + 7)

Question 1: A rectangular garden is 3 meters longer than it is wide. The area of the garden is 60 square meters. Write an equation for the area and factor it using the difference of squares.

Answer: Let width = x, then length = x + 3. Area = x(x + 3) = x² + 3x. To relate to difference of squares: rewrite as x² + 3x - 20 + 20. Not directly a difference of squares, but students should recognize quadratic form or factor directly.

Question 1: Factor the expression 4a² - 25b² completely.

Answer: (2a - 5b)(2a + 5b)

Question 2: Solve for x: x² - 36 = 0.

Answer: x = ±6

Question 1: Express 64 - y² as a product of two binomials.

Answer: (8 - y)(8 + y)

Question 2: Factor the expression 100a² - 81b².

Answer: (10a - 9b)(10a + 9b)

Question 1: Student incorrectly factors x² - 36 as (x - 6)(x - 6). What is wrong with this? Correct the factorization.

Answer: Incorrect as (x - 6)(x - 6) = x² - 12x +36, not x² -36. Correct factorization: (x - 6)(x + 6).