📝 Part 1: Identifying Like Terms

1. Circle the like terms in each expression:

a) 3x + 5y + 2x + 7y

b) 4a + 3b + 6a + 2c

c) 7m + 2n + 5m + 8n + 3

2. Which of the following are like terms? Check all that apply:

3x and 5x

2y and 4z

7a and 9a

5b and 3c

8m and 2m

🔢 Part 2: Combining Like Terms

3. Simplify these expressions by combining like terms:

a) 4x + 7x = ____________

b) 9y + 3y = ____________

c) 6a + 2a + 5a = ____________

d) 8m + 3n + 2m = ____________

e) 5p + 7q + 3p + 2q = ____________

4. Show your working to simplify: 12x + 5y + 8x + 3y

📐 Part 3: The Distributive Property

5. Use the distributive property to expand these expressions:

a) 3(x + 4) = ____________

b) 5(2y + 3) = ____________

c) 4(3a + 7) = ____________

d) 6(m + 2n) = ____________

6. Which expression is equivalent to 2(3x + 5)? Circle the correct answer:

5x + 7

6x + 10

6x + 5

2x + 10

7. Show your working to expand and simplify: 3(2x + 4) + 5x

🎯 Part 4: Mixed Practice

8. Simplify these expressions completely:

a) 7x + 3x + 2y + 5y = ____________

b) 4(a + 3) + 2a = ____________

c) 5m + 3(2m + 1) = ____________

d) 6p + 4q + 2(3p + q) = ____________

9. Match each expression on the left with its simplified form on the right:

1. 8x + 3x

2. 4(y + 2)

3. 5a + 2a + 3

4. 3(2m + 1) + m

A. 7a + 3

B. 4y + 8

C. 11x

D. 7m + 3

💭 Part 5: Problem Solving

10. Sarah has x dollars. Tom has 3 times as much money as Sarah plus $5 extra. Write an expression for the total amount of money they have together, then simplify it.

11. A rectangle has length (3x + 2) metres and width (x + 4) metres. Write an expression for the perimeter and simplify it. (Remember: Perimeter = 2 × length + 2 × width)

12. Explain in your own words what it means for two algebraic expressions to be equivalent: