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Expanding Single Brackets

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Expanding Single Brackets

Expanding Single Brackets

Algebraic expressions with brackets

📚 Part 1: Basic Expansion

Remember: To expand a(b + c), multiply the term outside the bracket by each term inside the bracket.

1. Expand the following expressions:

a) 3(x + 4) = _______________

b) 5(y - 2) = _______________

c) 2(3x + 7) = _______________

d) 4(2y - 5) = _______________

⚠️ Part 2: Working with Negative Signs

Careful: When the coefficient is negative, remember to multiply it by each term inside the bracket.

2. Expand these expressions involving negative coefficients:

a) -3(x + 5) = _______________

b) -2(4y - 3) = _______________

c) -6(2x + 1) = _______________

d) -4(3y - 7) = _______________

🔢 Part 3: Multiple Terms in Brackets

Challenge: Expand expressions with three or more terms inside the brackets.

3. Expand and simplify:

a) 3(x + 2y - 4) = _______________

b) 5(2x - y + 3) = _______________

c) -2(3x + 4y - 6) = _______________

d) 4(x - 2y + 5z) = _______________

🎯 Part 4: Multiple Choice - Common Mistakes

4. Which of the following correctly expands 3(2x - 4)?

6x - 4

6x - 12

3x - 12

5x - 7

5. What is the correct expansion of -5(x + 3)?

-5x + 3

-5x - 15

5x - 15

-5x + 15

🧮 Part 5: Problem Solving

6. A rectangle has length (3x + 2) metres and width 4 metres. Write an expression for the area of the rectangle in expanded form.
7. Sarah buys 5 packets of lollies. Each packet costs $(2x + 3). Write an expression for the total cost in expanded form.

⭐ Part 6: Extension Challenge

8. Expand and simplify: 2(3x + 4) - 5(x - 2)

Hint: Expand each bracket separately first, then combine like terms.

9. Expand and simplify: 3(2y - 1) + 4(y + 3)

💭 Part 7: Reflection

10. Explain in your own words why we need to multiply the coefficient by each term inside the bracket when expanding.
11. What is the most common mistake students make when expanding brackets? How can you avoid this mistake?

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