Question 1: Simplify the expression 3x + 5x.

Answer: 8x

Question 2: Combine like terms: 7a + 2a + 4a.

Answer: 13a

Question 3: Simplify 6y + 3y + y.

Answer: 10y

Question 4: Calculate 4x + 2x + 3x.

Answer: 9x

Question 1: Explain why combining 5y + 3z is incorrect if the goal is to simplify an expression with like terms.

Answer: Because y and z are different variables; they are not like terms, so they cannot be combined.

Question 2: A student simplifies 2a + 4b as 6a. Identify the mistake and correct it.

Answer: The mistake is treating unlike terms as like; they should not be combined. Correct form: 2a + 4b.

Question 3: If an expression has 3x + 2x + 4x, how many like terms are there, and what is the simplified form?

Answer: Three like terms; simplified form is 9x.

Question 1: A shop sells 3 apples for £2 and 5 oranges for £3. Write an expression for the total cost if buying x apples and y oranges, assuming positive coefficients.

Answer: 2/3 * 3x + 3/5 * 5y = 2x + 3y

Question 1: Write an expression with positive coefficients that simplifies to 5x + 7y + 3z. Explain your reasoning.

Answer: One possible expression is 2x + 3x + 4y + 3y + 2z + z. The coefficients are positive and the like terms combine to the given expression.

Question 2: Construct a polynomial with only positive coefficients and degree 3 that expands to 2a^3 + 3a^2 + 4a + 5.

Answer: Possible polynomial: (a + 1)^3 + 2a^2 + 3a + 4, which expands to a^3 + 3a^2 + 3a + 1 + 2a^2 + 3a + 4 = a^3 + 5a^2 + 6a + 5.

Question 1: A student simplifies 4x + 4y as 8x. What is the mistake? Correct the expression.

Answer: They incorrectly combined unlike terms. Correct expression: 4x + 4y.

Question 2: Identify the error in simplifying 6a + 2a + 3b as 11a and explain how to correctly combine them.

Answer: They combined unlike terms. Correct: 6a + 2a = 8a; 3b is separate.