Lesson that gives examples of how to factorise quadratic equations using the difference of 2 squares rule and the properties of perfect squares.

1. FACTORISING QUADRATICS
Difference of 2 squares and Perfect Squares

2. DIFFERENCE OF 2 SQUARES
• Investigate (expand):
(x − 5)(x + 5) =
(x + 2)(x − 2) =
(3x − 6)(3x + 6) =

3. DIFFERENCE OF 2 SQUARES
• Investigate (expand):
(x − 5)(x + 5) =
(x + 2)(x − 2) =
(3x − 6)(3x + 6) =

4. DIFFERENCE OF 2 SQUARES
• Investigate (expand):
2 2
(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25
(x + 2)(x − 2) =
(3x − 6)(3x + 6) =

5. DIFFERENCE OF 2 SQUARES
• Investigate (expand):
2 2
(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25
2 2
(x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4
(3x − 6)(3x + 6) =

6. DIFFERENCE OF 2 SQUARES
• Investigate (expand):
2 2
(x − 5)(x + 5) = x − 5x + 5x − 25 = x − 25
2 2
(x + 2)(x − 2) = x + 2x − 2x − 4 = x − 4
2
(3x − 6)(3x + 6) = 9x + 18x − 18x − 36
2
= x − 36

7. DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b

8. FACTORISING USING
DIFFERENCE OF 2 SQUARES
• Factorise
2
x −36

9. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
• Factorise
2
x −36

10. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
x −36

11. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
x −36
a=x

12. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
x −36
a=x b=6

13. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
x −36 = (x + 6)(x − 6)
a=x b=6

14. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
4x −25

15. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
4x −25
( 2x ) −5
2 2

16. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
4x −25
( 2x ) −5
2 2
a = 2x

17. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
4x −25
( 2x ) −5
2 2
a = 2x b=5

18. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
4x −25 = (2x + 5)(2x − 5)
( 2x ) −5
2 2
a = 2x b=5

19. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
3x −15

20. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
3x −15 2
( ) ( ) 2
3x − 15

21. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
3x −15 2
( ) ( ) 2
3x − 15
a = 3x

22. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
3x −15 2
( ) ( ) 2
3x − 15
a = 3x
b = 15

23. FACTORISING USING
DIFFERENCE OF 2 SQUARES
2 2
(a + b)(a − b) = a − b
2 2
a − b = (a + b)(a − b)
• Factorise
2
3x −15 = ( 3x + 15 )( 3x − 15 )
2
( ) ( ) 2
3x − 15
a = 3x
b = 15

24. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)

25. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)

26. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

27. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)
a=x
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

28. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)
a=x b = −5
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

29. PERFECT SQUARES
• Investigate (expand):
2
(x − 5) = (x − 5)(x − 5)
a=x b = −5
2ab = 2 × x × (−5)
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

30. PERFECT SQUARES
• Factorise
2
x − 8x + 16

31. PERFECT SQUARES
• Factorise
2
x − 8x + 16
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

32. PERFECT SQUARES
• Factorise
2
x − 8x + 16
a=x
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

33. PERFECT SQUARES
• Factorise
2
x − 8x + 16
a=x b = −4
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

34. PERFECT SQUARES
• Factorise
2
x − 8x + 16
a=x b = −4
2ab = 2 × x × (−4)
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

35. PERFECT SQUARES
• Factorise
2 2
x − 8x + 16 = (x − 4)
a=x b = −4
2ab = 2 × x × (−4)
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

36. PERFECT SQUARES
• Factorise
2
x + 2 5x + 5

37. PERFECT SQUARES
• Factorise
2
x + 2 5x + 5
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

38. PERFECT SQUARES
• Factorise
2
x + 2 5x + 5
a=x
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

39. PERFECT SQUARES
• Factorise
2
x + 2 5x + 5
a=x b= 5
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

40. PERFECT SQUARES
• Factorise
2
x + 2 5x + 5
a=x b= 5
2ab = 2 × x × 5
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b

41. PERFECT SQUARES
• Factorise
2 2
x + 2 5x + 5 = (x + 5 )
a=x b= 5
2ab = 2 × x × 5
2 2 2
(a + b) = a + 2ab + b
2 2 2
(a − b) = a − 2ab + b