Question 1: Simplify the expression: a² - b² when a = 5 and b = 3.

Answer: 16

Question 2: Factor the expression: 49 - x².

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

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

Answer: x² - 16

Question 4: Calculate the value of 64 - 36 when a = 8 and b = 6, using the difference of squares.

Answer: 28

Question 5: Identify the difference of squares in the expression 81 - y².

Answer: Yes, it is a difference of squares since it can be written as (9)^2 - y^2.

Question 6: Factor completely: 100 - 36x².

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

Question 7: A rectangle has length (x + 2) and width (x - 2). Write an expression for its area and factor it using difference of squares.

Answer: Area = (x + 2)(x - 2) = x² - 4

Question 8: Construct a pair of binomials that multiply to 25 - p².

Answer: (5 - p)(5 + p)

Question 9: Find the value of the expression when a = 7 and b = 2: a² - b².

Answer: 45

Question 10: Express the difference of squares for 144 - 81 as a product of two binomials.

Answer: (12 - 9)(12 + 9) or 3(4 - 3)(4 + 3)

Question 11: Identify and correct the mistake: Simplify (x + 3)(x - 3) = x² + 9.

Answer: Incorrect; it should be x² - 9, not x² + 9.