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Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions

Algebraic expressions illustration

📚 Part 1: Combining Like Terms

1. Simplify the following expressions by combining like terms:

a) 5x + 3x = ________________

b) 7a + 2b + 4a = ________________

c) 8m - 3m + 6n = ________________

d) 2y + 5 + 7y - 3 = ________________

2. Which of the following expressions are equivalent to 9x + 4y?

3x + 6x + 4y

9x + 2y + 2y

13xy

5x + 4x + y + 3y

3. Circle the like terms in this expression: 4a + 7b + 2a + 9c + 5b

🔢 Part 2: Distributive Property

4. Expand the following expressions using the distributive property:

a) 3(x + 5) = ________________

b) 4(2a - 3) = ________________

c) -2(3m + 7) = ________________

d) 6(4p - 2q + 1) = ________________

5. What is the expanded form of 5(2x + 3)?

7x + 8

10x + 15

10x + 3

5x + 15

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

🎯 Part 3: Mixed Practice

7. Simplify these expressions completely:

a) 2(3x + 1) + 4x = ________________

b) 5(a - 2) + 3a + 7 = ________________

c) 4(2m + 3n) - 2m + n = ________________

8. A rectangle has length (3x + 2) metres and width 4 metres. Write a simplified expression for its perimeter.
9. Explain in your own words what it means for two algebraic expressions to be equivalent:
10. Challenge: Simplify 2(3x + 4) + 3(x - 1) - 5x

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