The document provides steps for factorising expressions: 1) Look for common factors and divide them out 2) Factorise the difference of two squares using the form (a-b)(a+b) 3) Factorise quadratic trinomials into the product of two binomials using the forms x2 + (a+b)x + ab or (x+a)(x+b) Examples are provided for each type of factorisation.

1. Factorising

2. Factorising
1) Look for a common factor

3. Factorising
1) Look for a common factor
2) (i) 2 terms
 difference of two squares

4. Factorising
1) Look for a common factor
2) (i) 2 terms
 difference of two squares
 sum/difference of two cubes

5. Factorising
1) Look for a common factor
2) (i) 2 terms
 difference of two squares
 sum/difference of two cubes
(ii) 3 terms
 quadratic trinomial

6. Factorising
1) Look for a common factor
2) (i) 2 terms
 difference of two squares
 sum/difference of two cubes
(ii) 3 terms
 quadratic trinomial
(iii) 4 terms
 grouping in pairs

7. 1. Common Factor
factorising
=
dividing by common factor

8. 1. Common Factor
factorising
e.g. (i ) ax  bx
=
dividing by common factor

9. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
dividing by common factor

10. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x dividing by common factor

11. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor

12. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny

13. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 

14. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 

15. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 

16. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1

17. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1

18. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75

19. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75 =3  y 2  25 

20. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75 =3  y 2  25 
=3  y  5  y  5 

21. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75 =3  y 2  25 
=3  y  5  y  5 
(iii ) 5 x  5 y  x 2  y 2

22. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75 =3  y 2  25 
=3  y  5  y  5 
(iii ) 5 x  5 y  x 2  y 2 =5  x  y    x  y  x  y 

23. 1. Common Factor
factorising
e.g. (i ) ax  bx  x  a  b 
=
(ii ) 5 x 2  10 x  5 x  x  2  dividing by common factor
(iii ) mx  nx  my  ny  x  m  n   y  m  n 
  m  n  x  y 
2. Difference of Two Squares
a 2  b 2   a  b  a  b 
e.g. (i ) 16x 2  1 =  4 x  1 4 x  1
(ii ) 3 y 2  75 =3  y 2  25 
=3  y  5  y  5 
(iii ) 5 x  5 y  x 2  y 2 =5  x  y    x  y  x  y 
=  x  y  5  x  y 

24. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab

25. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18

26. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
9

27. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9

28. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3

29. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3 3
  4

30. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3 3
  t  3 t  1   4

31. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3 3
  t  3 t  1   4
(iii ) x 2  5 xy  4 y 2

32. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3 3
  t  3 t  1   4
(iii ) x 2  5 xy  4 y 2   4 y 2
  5 y

33. 3. Quadratic Trinomial
a) Monic Quadratic
 x  a  x  b   x 2   a  b  x  ab
e.g. (i ) x 2  9 x  18   18
  x  6  x  3 9
(ii ) t 2  4t  3 3
  t  3 t  1   4
(iii ) x 2  5 xy  4 y 2   4 y 2
  x  y  x  4 y    5 y

34. b) Splitting the Middle

35. b) Splitting the Middle
e.g. (i ) 3x 2  4 x  7

36. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
4 7  3

37. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3

38. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1

39. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 

40. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12

41. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12   24
  5

42. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12   24
 2 x 2  8 x  3 x  12   5

43. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12   24
 2 x 2  8 x  3 x  12   5
 2 x  x  4  3 x  4

44. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12   24
 2 x 2  8 x  3 x  12   5
 2 x  x  4  3 x  4
  x  4  2 x  3

45. b) Splitting the Middle
Multiply the constant by the
e.g. (i ) 3x  4 x  7
2   21
coefficient of x squared
 3x 2  3x  7 x  7   4 7  3
 3 x  x  1  7  x  1
  x  1 3 x  7 
(ii ) 2 x 2  5 x  12   24
 2 x 2  8 x  3 x  12   5
 2 x  x  4  3 x  4
  x  4  2 x  3
Exercise 1C; 1e, 2f, 3d, 4ejo, 5adhkn, 6ace etc, 7ace etc, 8*bdfij