Question 1: Factor the expression: x^2 - 16.

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

Question 2: Identify the pattern in the sequence: 9, 16, 25, 36, ... and predict the next term.

Answer: 49

Question 3: Express as a difference of two squares: 49 - 25.

Answer: (7 - 5)(7 + 5) = 2 * 12 = 24

Question 4: Construct two binomials that multiply to give x^2 - 81.

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

Question 5: What is the pattern in the difference of squares for the numbers 1, 4, 9, 16, 25?

Answer: They are squares of natural numbers, and the differences between consecutive squares increase by 2 each time.

Question 6: Simplify: x^2 - 36 = (x - 6)(x + 6). Identify the pattern used.

Answer: Difference of squares pattern

Question 7: Given the polynomial x^4 - 81, factor it completely using difference of squares.

Answer: (x^2 - 9)(x^2 + 9) = (x - 3)(x + 3)(x^2 + 9)

Question 8: Identify the mistake: Factor x^2 - 25 as (x - 5)(x - 5). Correct the error.

Answer: The correct factorization is (x - 5)(x + 5).

Question 9: Solve for x: x^2 - 49 = 0. Show all steps.

Answer: x^2 = 49 x = ±7

Question 10: Plot the graph of y = x^2 - 64 on the grid.

Answer: Students will draw the parabola crossing x-axis at ±8.

Question 11: Construct an algebraic expression representing the difference of squares that simplifies to x^4 - 16.

Answer: (x^2 - 4)(x^2 + 4)

Question 12: Challenge: Prove that for any integer n, n^4 - 16 can be expressed as a product of two difference of squares.

Answer: n^4 - 16 = (n^2 - 4)(n^2 + 4) = (n - 2)(n + 2)(n^2 + 4)