Question 1: Expand the expression: (x + 3)(x + 5).

Answer: x^2 + 8x + 15

Question 2: Simplify the expansion of (x - 4)(x + 2).

Answer: x^2 - 2x - 8

Question 3: Expand and simplify: (x + 7)(x + 1).

Answer: x^2 + 8x + 7

Question 4: Use the FOIL method to expand (x + 2)(x + 4).

Answer: x^2 + 6x + 8

Question 5: Factor the quadratic expression: x^2 + 5x + 6. Then write it as a product of two brackets in the form (x + a)(x + b).

Answer: (x + 2)(x + 3)

Question 6: Expand (x + a)(x + b) where a = 4 and b = -3. Write your answer in simplified form.

Answer: x^2 + x - 12

Question 7: A rectangle has sides of length (x + 2) and (x + 3). Write an expression for its area by expanding the brackets.

Answer: x^2 + 5x + 6

Question 8: Expand (x - 5)(x + 6) and identify the coefficient of x.

Answer: x^2 + x

Question 9: Expand (x + 8)(x - 2) using the FOIL method.

Answer: x^2 + 6x - 16

Question 10: Identify the common mistake in expanding (x + 3)(x + 5) as x^2 + 8x + 15. Why is this wrong?

Answer: The mistake is adding the constants instead of multiplying the inner terms. They should be multiplied: 3×5=15, not added.

Question 11: Challenge: Find the expansion of (x + a)(x + b) when a and b are algebraic expressions: (x + 2a)(x + 3b).

Answer: x^2 + (2a + 3b)x + 6ab