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Expanding Algebraic Expressions

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Expanding Algebraic Expressions worksheet preview
Expanding Algebraic Expressions

Expanding Algebraic Expressions

Algebraic expressions illustration

📐 Part 1: Distributive Property Warm-Up

1. Apply the distributive property to expand these numerical expressions:

a) 3 × (4 + 5) = ___________

b) 2 × (6 + 3) = ___________

c) 5 × (8 - 2) = ___________

2. Now apply the distributive property to these simple algebraic expressions:

a) 2(x + 3) = ___________

b) 4(y + 5) = ___________

c) 3(a - 2) = ___________

🔢 Part 2: Single Bracket Expansion

3. Expand and simplify the following expressions. Show your working:

a) 3(x + 4) = ___________

b) 2(2x + 7) = ___________

c) 5(3x - 1) = ___________

d) 4x(x + 2) = ___________

4. Which of the following shows the correct expansion of 3(2x + 5)?

6x + 5

6x + 15

3x + 15

5x + 8

📊 Part 3: Area Model for Double Brackets

5. Use the area model to expand (x + 3)(x + 2). Draw and label the rectangle below:
6. From your area model above, write the expanded form:

(x + 3)(x + 2) = ___________

7. Expand the following double bracket expressions using any method. Show your working:

a) (x + 4)(x + 1) = ___________

b) (x + 5)(x - 2) = ___________

c) (2x + 3)(x + 4) = ___________

🧮 Part 4: Complex Expressions

8. Expand and simplify these more complex expressions:

a) 3x(x + 1) - (x - 2) = ___________

b) 4(x - 2) + 3(2x + 1) = ___________

c) (x + 2)(x - 3) + 2(x + 1) = ___________

9. Check all the common mistakes students make when expanding expressions:

Forgetting to multiply both terms in the bracket

Not combining like terms after expansion

Incorrectly handling negative signs

Adding instead of multiplying

💭 Part 5: Understanding and Reflection

10. In your own words, explain what the distributive property means in algebra:
11. Match each expression with its correct expanded form:
1. 2(x + 5)
2. (x + 3)(x + 1)
3. 3x(x - 2)
4. (2x + 1)(x + 4)
A. 2x² + 9x + 4
B. x² + 4x + 3
C. 3x² - 6x
D. 2x + 10
12. Challenge Problem: A rectangle has length (2x + 3) metres and width (x + 1) metres. Write an expression for its area and expand it:

Area = ___________

13. Describe one strategy that helps you remember how to expand double brackets:

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