📚 Part 1: Simplifying and Expanding Expressions

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

b) 4(2x - 3) + 6 = ___________

c) 7x² - 3x² + 5x = ___________

a) 5(x + 4) = ___________

b) -3(2x - 7) = ___________

c) x(x + 6) = ___________

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

b) 3(2x + 5) - 2(x + 3) = ___________

✏️ Part 2: Algebraic Manipulation Practice

a) 6x/3 = ___________

b) 8x²/4x = ___________

c) (15x + 10)/5 = ___________

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

b) (x - 4)(x + 5) = ___________

a) The perimeter: ___________

b) The area: ___________

🔍 Part 3: IB-Style Investigation

The distributive property states that a(b + c) = ab + ac. But does this work with powers?

Part A: Test whether x(y + z)² = xy² + xz² by substituting x = 2, y = 3, z = 4:

Part B: Now expand (y + z)² first, then multiply by x. Show your working:

Part C: Based on your calculations, explain why the distributive property doesn't work directly with powers. What is the correct way to expand x(y + z)²?

Part D: Create your own example to test whether 2(a + b)³ = 2a³ + 2b³. Show that this is false and provide the correct expansion.