Question 1: Simplify the expression: 36 - 25.

Answer: 11

Question 2: Express the difference of squares: 49 - 16 as a product of two binomials.

Answer: (7 + 4)(7 - 4)

Question 3: Calculate the value of (15 + 7)(15 - 7).

Answer: 176

Question 4: Factor the expression: x² - 36.

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

Question 5: A shop sells two types of goods. The price difference between two items is $25, and one item costs $49. Write an expression for the squared difference if the prices are represented as a and b, where a = 49 and b is the other item's price.

Answer: a² - b²

Question 6: If the price of a product increases from $64 to $81, use the difference of squares to find the change in price squared.

Answer: (9)(9) = 81

Question 7: A finance company calculates the profit difference between two investments as 100 - 64. Express this difference as a product of two binomials.

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

Question 8: A business measures the variation in revenue as the difference between two squares, 121 - 81. Find the two possible revenue figures if the difference of squares factors are known.

Answer: 11 + 9 or 11 - 9

Question 9: Construct a problem where the difference of two squares models the profit difference between two stores with revenues of $144 and $100. What is the algebraic expression for their profit difference?

Answer: a² - b²

Question 10: A company notices that the square of its highest revenue is 225, and the square of its lowest revenue is 121. Find the difference in revenues using the difference of squares.

Answer: 14

Question 11: Identify and correct the mistake: Simplify x² - 25 as (x + 5)(x + 5).

Answer: Correct answer is (x + 5)(x - 5)