Factorising Difference of Two Squares
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Factorising Difference of Two Squares
Year 10 Mathematics Mixed Ability Class 55 minutes
Learning Intentions (WALT)
We Are Learning To understand and apply the factorisation method for the difference of two squares We Are Learning To recognise algebraic expressions that can be written as a difference of squares We Are Learning To use factorised expressions to simplify or solve algebraic problems
Success Criteria
I can identify expressions that fit the form a² - b² I can factorise expressions into (a-b)(a+b) correctly I can solve simple equations involving difference of squares I can explain the steps and reasoning behind the factorisation process
Key Vocabulary
Factorise - to write as a product of factors Difference of squares - expression in form a² - b² Binomial - algebraic expression with two terms Square number - number that is the square of an integer Expression vs Equation - expression has no equals sign
Difference of Squares Formula
Example 1: x² - 9 = x² - 3² = (x - 3)(x + 3) Example 2: 25 - y² = 5² - y² = (5 - y)(5 + y) Example 3: 4x² - 1 = (2x)² - 1² = (2x - 1)(2x + 1) Check by expanding: (x - 3)(x + 3) = x² - 9 ✓
Guided Practice Examples
Example 1: x² - 9 = x² - 3² = (x - 3)(x + 3) Example 2: 25 - y² = 5² - y² = (5 - y)(5 + y) Example 3: 4x² - 1 = (2x)² - 1² = (2x - 1)(2x + 1) Check by expanding: (x - 3)(x + 3) = x² - 9 ✓
Collaborative Group Task
Work in groups of 3-4 students Each group gets a set of expressions to factorise Use algebra tiles if needed for visual support Discuss your reasoning with group members Be ready to explain one solution to the class
Independent Practice - Differentiated
Foundation Level: Factorise x² - 4, 9 - y², 16 - z² Standard Level: Factorise 4x² - 25, 49 - 9y², x² - 36 Extension Level: Factorise 25x² - 16y², solve 4x² - 9 = 0 Use scaffolded worksheets with step-by-step prompts
Extension Challenge
Advanced Problem: If 16x² - 9 = 0, find the value(s) of x Method 1: Factorise first, then solve Method 2: Use the quadratic formula Challenge: Explain why there are two solutions Real-world connection: Where might this apply?
Plenary and Reflection
Exit Slip Question: Factorise x² - 25 and explain your steps Reflection: What was the most challenging part of today's lesson? Quick Check: Can you identify when NOT to use difference of squares? Peer Discussion: Share one strategy that helped you today
Summary and Next Steps
Today we learned: a² - b² = (a - b)(a + b) Key skill: Identifying perfect squares in expressions Next lesson: Solving quadratic equations by factorisation Homework: Complete practice worksheet (differentiated levels available) Extension reading: Research other algebraic identities