📚 Part 1: Area Method Expansion

1. Use the area method to expand (x + 3)(x + 2). Draw the rectangle and fill in each section:

Expanded form: _________________

2. Expand using the area method: (2x + 1)(x + 4)

Simplified answer: _________________

3. Which property allows us to expand (a + b)(c + d) = ac + ad + bc + bd?

Commutative property

Associative property

Distributive property

Identity property

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

✏️ Part 2: Properties and Factorising

5. Complete the following to show the distributive property:

3(x + 4) = 3 × _____ + 3 × _____ = _____

6. Factorise the following expressions by finding the highest common factor:

a) 6x + 9 = _____(_____ + _____)

b) 4x² + 8x = _____(_____ + _____)

7. Which of these expressions are equivalent to 2x + 6? Tick all that apply:

2(x + 3)

x + 3 + x + 3

(x + 6) + x

6 + 2x

8. Expand and simplify: (x + 3)²

9. A rectangular garden has length (x + 4) metres and width (x + 1) metres. Write an expression for the total area and expand it:

10. Extension: Expand and simplify (2x + 3)(x² + x - 1)

11. Explain in your own words why the area method works for expanding algebraic expressions: