Question 1: Simplify the expression: 3x² + 2x².

Answer: 5x²

Question 2: Rearrange the formula to make x² the subject: y = 4x² + 7.

Answer: x² = (y - 7)/4

Question 3: If x = 3, what is the value of x²?

Answer: 9

Question 4: Calculate: (2x + 1)² when x = 4.

Answer: 81

Question 1: A square has an area of 49 cm². Find the length of one side, and explain how squaring relates to the area.

Answer: Side length = 7 cm; area = side², so side = √area = √49 = 7

Question 2: Rewrite the formula z = 5x² + 3 for x².

Answer: x² = (z - 3)/5

Question 3: If y = 16, what are the possible values of x if y = 4x²?

Answer: x = ±2

Question 1: A gardener is planting square patches of grass, each with an area of 144 m². What is the length of each side? How does squaring help in determining this?

Answer: Side length = 12 m; because area = side², so side = √144 = 12

Question 1: Solve for x in the equation: 2x² - 8 = 0. Show all steps and explain any common mistakes.

Answer: x² = 4; x = ±2

Question 2: A rectangle's length is twice its width. If the area is 100 cm², find the length and width. Show your reasoning.

Answer: Let width = w; length = 2w; area = w * 2w = 2w² = 100; w² = 50; w = √50 ≈ 7.07; length ≈ 14.14 cm

Question 1: Expand: (x + 3)².

Answer: x² + 6x + 9

Question 2: Identify the error in the student's work: Simplify 2x² + 3x² as 5x.

Answer: Incorrect; 2x² + 3x² = 5x², not 5x

Question 1: A student incorrectly rewrites y = 4x² as y = (4x)². Identify the mistake and explain the correct interpretation.

Answer: Mistake: (4x)² = 16x², which is different from 4x²; correct: 4x² is 4 times x², not (4 times x)²

Question 2: A student claims that (x + 2)² = x² + 4. Is this correct? If not, correct the mistake.

Answer: Incorrect; (x + 2)² = x² + 4x + 4