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Algebraic Expressions Worksheet

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Algebraic Expressions Worksheet worksheet preview

Algebraic Expressions Worksheet

Algebraic expressions illustration

📚 Part 1: Simplifying and Expanding

1. Simplify these expressions by collecting like terms:

a) 3x + 5x - 2x = ______________

b) 4a + 7b - 2a + 3b = ______________

c) 2x² + 5x - x² + 3x = ______________

2. Expand using the distributive property:

a) 3(x + 4) = ______________

b) -2(3y - 5) = ______________

c) x(2x + 7) = ______________

3. Use the area method to expand (x + 3)(x + 2). Draw your working in the box below:
4. Which property is shown in each example? Choose from: Commutative, Associative, Distributive

a) 5x + 3x = 3x + 5x → Property: ________________

b) 2(x + 4) = 2x + 8 → Property: ________________

c) (2x + 3x) + 5x = 2x + (3x + 5x) → Property: ________________

✏️ Part 2: Factorising

5. Factorise by taking out the common factor:

a) 6x + 9 = ______________

b) 4x² + 8x = ______________

c) 15y - 10 = ______________

6. Factorise these quadratic expressions:

a) x² + 5x + 6 = ______________

b) x² - 7x + 12 = ______________

7. Show your working to factorise x² + 7x + 10 using any method:

🌟 Part 3: Problem Solving

8. A rectangular garden has length (x + 5) metres and width (x + 2) metres.

a) Write an expression for the area: ______________

b) Expand your expression: ______________

c) If x = 3, what is the actual area? ______________ m²

9. Explain in your own words why the distributive property works. Use an example with numbers and algebra:
10. Extension Challenge: Factorise 2x² + 7x + 3

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