Question 1: Factor the expression a² - 16.

Answer: (a - 4)(a + 4)

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

Answer: x² - 25

Question 3: Simplify the expression a² - b² given that a = 7 and b = 3.

Answer: 40

Question 4: Identify the difference of squares in the set of expressions below: (i) x² + 9 (ii) 25 - y² (iii) 4a² - 49

Answer: (ii), (iii)

Question 5: Construct a binomial factorization for x² - 36.

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

Question 6: Solve for x: x² - 49 = 0.

Answer: x = ±7

Question 7: Factor the quadratic: x² - 6x - 7.

Answer: (x - 7)(x + 1)

Question 8: A rectangle's length is (x + 3) units and width is (x - 3) units. Write an expression for its area and simplify.

Answer: x² - 9

Question 9: Construct a factorization for 4a² - 25.

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

Question 10: Identify and correct the mistake in the following: The expression a² + 9 can be written as (a + 3)(a - 3).

Answer: The expression a² + 9 cannot be factored as (a + 3)(a - 3); it's a sum of squares, which doesn't factor over real numbers.

Question 11: Challenge: Factor the expression 9a⁴ - 16b⁴.

Answer: (3a² - 4b²)(3a² + 4b²)