Factorising Difference of Two Squares
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Factorising Difference of Two Squares
Year 10 Mathematics WALT: Recognise and factorise expressions of the form a² - b² Success Criteria: Identify, factorise, and apply difference of squares
What Are Perfect Squares?
Numbers that result from squaring whole numbers Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 In algebra: x², 4x², 9y², 16a² Can you identify more perfect squares?
Can You Spot the Pattern?
Look at these expressions: 25 - 9 x² - 16 49 - y² What do they all have in common?
The Difference of Two Squares Formula
General form: a² - b² = (a - b)(a + b) This is called the difference of two squares Works for any values of a and b Let's verify: (a - b)(a + b) = a² + ab - ab - b² = a² - b²
Guided Practice Together
Example 1: x² - 9 Step 1: Identify a² = x², so a = x Step 2: Identify b² = 9, so b = 3 Step 3: Apply formula: (x - 3)(x + 3) Your turn: Try 25 - y²
More Examples to Try
{"left":"Example: 16 - x²\na² = 16, so a = 4\nb² = x², so b = x\nAnswer: (4 - x)(4 + x)","right":"Example: 4y² - 25\na² = 4y², so a = 2y\nb² = 25, so b = 5\nAnswer: (2y - 5)(2y + 5)"}
Your Turn - Independent Practice
Factorise these expressions: 1. x² - 49 2. 81 - y² 3. 9a² - 16 4. 100 - 25b² Extension: Solve x² - 36 = 0
Summary and Next Steps
Today we learned to factorise a² - b² Key pattern: difference of two perfect squares Formula: a² - b² = (a - b)(a + b) Next lesson: Using factorisation to solve equations Exit ticket: Factorise one expression from today