Question 1: Expand (x + 3).

Answer: x + 3

Question 2: Expand 2(a + 4).

Answer: 2a + 8

Question 3: Expand 5(n + 2).

Answer: 5n + 10

Question 1: Expand 3(x + 7).

Answer: 3x + 21

Question 2: Expand 4(2x + 5).

Answer: 8x + 20

Question 3: Expand 6(a + 3).

Answer: 6a + 18

Question 1: If 3(x + 4) = 21, what is the value of x?

Answer: x = 5

Question 2: Given that 2a + 6 = 18, write an expression for expanding 2(a + 3). Then solve for a.

Answer: 4a + 6, a = 3

Question 3: Explain why expanding 5(b + 2) always results in a positive coefficient for b.

Answer: Because 5 is positive, when expanding 5(b + 2), the coefficient of b is 5, which is positive regardless of the value of b.

Question 1: A gardener plants 4 rows of flowers, with each row having (x + 2) flowers. Write an expression for the total number of flowers and evaluate if x = 3.

Answer: Total = 4(x + 2) = 4x + 8; for x=3, total=4(3)+8=20

Question 2: A car travels 5 times the distance of x kilometers plus 10 km. Express this as an algebraic expression, then find the distance when x=7.

Answer: Distance = 5x + 10; for x=7, distance=5(7)+10=45 km

Question 1: Expand (x + 4)(x + 5) and identify the coefficient of x in the expanded form.

Answer: x^2 + 9x + 20; coefficient of x is 9

Question 2: Given the expression 3(a + 2) + 4(a + 5), simplify fully and state the coefficient of a.

Answer: 7a + 26; coefficient of a is 7

Question 1: A student expands (x + 3) as x + 3. Is this correct? If not, what is the correct expansion?

Answer: No, the correct expansion is x + 3, which is correct for (x+3); but if mistake was thinking expansion is just the sum, clarify that the expansion is x + 3, which is correct.

Question 2: Expand 2(x + 2) but incorrectly write the answer as 2x + 2. Correct and explain the mistake.

Answer: Correct expansion: 2x + 4; mistake was omitting the multiplication of 2 by 2.