Factorising Difference of Two Squares

Factorising Difference of Two Squares

Year 10 Mathematics WALT: Understand and apply factorisation of a² - b² Success Criteria: Identify, factorise, and solve using difference of squares

WALT - We Are Learning To

Understand and apply the factorisation method for the difference of two squares Recognise algebraic expressions that can be written as a difference of squares Use factorised expressions to simplify or solve algebraic problems Explain the steps and reasoning behind the factorisation process

Warm-Up: Quick Recall

What is 7²? What is √49? Is 36 a perfect square? What does (x + 3)(x - 3) expand to?

What is Difference of Two Squares?

A special algebraic pattern: a² - b² Both terms must be perfect squares Connected by a minus sign Examples: x² - 9, 25 - y², 4x² - 1 Can always be factorised as (a - b)(a + b)

The Factorisation Formula

Guided Practice

Work through these examples together: Example 1: x² - 16 Example 2: 49 - y² Example 3: 9x² - 4 Check your factorisation by expanding

Independent Practice - Differentiated Tasks

{"left":"Foundation Level: Factorise x² - 4, y² - 25, 9 - z²\nStandard Level: Factorise 4x² - 9, 16 - y², 25x² - 1","right":"Extension Level: Solve 9x² - 16 = 0, Factorise 49a² - 36b²"}

Plenary & Key Takeaways

The pattern: a² - b² = (a - b)(a + b) Always check both terms are perfect squares Remember the minus sign between terms Verify your answer by expanding This technique helps solve quadratic equations Next lesson: Solving equations using factorisation