1. Created by Mr. Lafferty@mathsrevision.com
Algebraic Operations
Factors / HCF
Common Factors
Difference of Squares
Factorising Trinomials (Quadratics)
Factor Priority
31-Mar-17
Created by Mr.

2. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S3
Credit
Q1. Multiply out
(a) a (4y – 3x) (b) (2x-1)(x+4)
Q2. True or false
Q3. Write down all the number that divide
into 12 without leaving a remainder.
31-Mar-17
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3. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Using Factors
Learning Intention
Success Criteria
To explain that a factor divides into a number without leaving a remainder
To explain how to find Highest Common Factors
To identify factors using factor pairs
Find HCF for two numbers by comparing factors.
31-Mar-17
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4. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Factors
Example : Find the factors of 56.
Numbers that divide into 56 without leaving a remainder
F56 = 1 and 56
2 and 28
4 and 14
7 and
31-Mar-17
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5. Factors Highest Common Factor Largest Same Number
Credit
Highest Common Factor
Highest
Common
Factor
Largest
Same
Number
We need to write out all factor pairs in order to find
the Highest Common Factor.
31-Mar-17
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6. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Highest Common Factor
Example : Find the HCF of 8 and 12.
F8 = 1 and 8
2 and 4
F12 = 1 and 12
2 and 6
3 and 4
HCF = 4
31-Mar-17
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7. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Highest Common Factor
Example : Find the HCF of 4x and x2.
F4x = 1, and 4x
Fx2 = 1 and x2
2 and 2x
x and x
4 and x
HCF = x
Example : Find the HCF of 5 and 10x.
F5 = 1 and 5
F10x = 1, and 10x
2 and 5x
HCF = 5
5 and 2x
31-Mar-17
Created by Mr.
10 and x

8. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Highest Common Factor
Example : Find the HCF of ab and 2b.
F ab = 1 and ab
a and b
F2b = 1 and 2b
2 and b
HCF = b
Example : Find the HCF of 2h2 and 4h.
F 2h2 = 1 and 2h2
2 and h2 , h and 2h
F4h = 1 and 4h
2 and 2h
4 and h
HCF = 2h
31-Mar-17
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9. Created by Mr. Lafferty@mathsrevision.com
Factors S3
Credit
Find the HCF for these terms 8w
(a) 16w and 24w
9y2 and 6y
(c) 4h and 12h2
(d) ab2 and a2b 3y 4h ab
31-Mar-17
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10. First Column in each Question
Factors S3
Credit
Now try Ex 2.1 & 3.1
First Column in each Question
Ch5 (page 86)
31-Mar-17
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11. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S3
Credit
Q1. Expand out
(a) a (4y – 3x) -2ay (b) (x + 5)(x - 5)
Q2. Write out in full
Q3. True or False all the factors of 5x2 are
1, x, 5
31-Mar-17
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12. Created by Mr. Lafferty@www.mathsrevision.com
Factorising S3
Credit
Using Factors
Learning Intention
Success Criteria
To show how to factorise terms using the Highest Common Factor and one bracket term.
To identify the HCF for given terms.
Factorise terms using the HCF and one bracket term.
31-Mar-17
Created by Mr.

13. Factorising Example Factorise 3x + 15 1. Find the HCF for 3x and 15 3
Check by multiplying out the bracket to get back to where you started
Factorising S3
Credit
Example
Factorise 3x + 15
1. Find the HCF for 3x and 15 3
2. HCF goes outside the bracket
3( )
To see what goes inside the bracket
divide each term by HCF
3x ÷ 3 = x
15 ÷ 3 = 5
3( x + 5 )
31-Mar-17
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14. Factorising Example Factorise 4x2 – 6xy
Check by multiplying out the bracket to get back to where you started
Factorising S3
Credit
Example
Factorise 4x2 – 6xy
1. Find the HCF for 4x2 and 6xy 2x
2. HCF goes outside the bracket
2x( )
To see what goes inside the bracket
divide each term by HCF
4x2 ÷ 2x =2x
6xy ÷ 2x = 3y
2x( 2x- 3y )
31-Mar-17
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15. Created by Mr. Lafferty@mathsrevision.com
Factorising S3
Credit
Factorise the following :
3(x + 2)
(a) 3x + 6
4xy – 2x
6a + 7a2
(d) y2 - y
Be careful !
2x(2y – 1)
a(6 + 7a)
y(y – 1)
31-Mar-17
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16. Created by Mr. Lafferty@www.mathsrevision.com
Factorising S3
Credit
Now try Ex 4.1 & 4.2
First 2 Columns only
Ch5 (page 88)
31-Mar-17
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17. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S3
Credit
Q1. In a sale a jumper is reduced by 20%. The sale price is £32.
Show that the original price was £40
Q2. Factorise 3x2 – 6x
Q3. Write down the arithmetic operation
associated with the word ‘difference’.
31-Mar-17
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18. Created by Mr. Lafferty@www.mathsrevision.com
Difference of
Two Squares S3
Credit
Learning Intention
Success Criteria
To show how to factorise the special case of the difference of two squares.
Recognise when we have a difference of two squares.
Factorise the difference of two squares.
31-Mar-17
Created by Mr.

19. Difference of Two Squares
Credit
When an expression is made up of
the difference of two squares
then it is simple to factorise
The format for the difference of two squares
a2 – b2
First
square term
Second
square term
Difference
31-Mar-17
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20. Difference of Two Squares
Credit
Check by multiplying out the bracket to get back to where you started
a2 – b2
First
square term
Second
square term
Difference
This factorises to
( a + b )( a – b )
Two brackets the same except for + and a -
31-Mar-17
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21. Always the difference sign -
Difference of
Two Squares S3
Credit
Keypoints
Format a2 – b2
Always the difference sign -
( a + b )( a – b )
31-Mar-17
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22. Difference of Two Squares
Credit
Factorise using the difference of two squares
(x + 7 )( x – 7 )
(a) x2 – 72
w2 – 1
9a2 – b2
(d) 16y2 – 100k2
( w + 1 )( w – 1 )
( 3a + b )( 3a – b )
( 4y + 10k )( 4y – 10k )
31-Mar-17
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23. Difference of Two Squares
Credit
Trickier type of questions to factorise.
Sometimes we need to take out a common factor
and then use the difference of two squares.
Example
Factorise 2a2 - 18
First take out common factor
2(a2 - 9)
Now apply the difference of two squares
2( a + 3 )( a – 3 )
31-Mar-17
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24. Difference of Two Squares
Credit
Factorise these trickier expressions.
6(x + 2 )( x – 2 )
(a) 6x2 – 24
3w2 – 3
8 – 2b2
(d) 27w2 – 12
3( w + 1 )( w – 1 )
2( 2 + b )( 2 – b )
3(3 w + 2 )( 3w – 2 )
31-Mar-17
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25. Created by Mr. Lafferty@www.mathsrevision.com
Difference of
Two Squares S3
Credit
Now try Ex 5.1 & 5.2
First 2 Columns only
Ch5 (page 90)
31-Mar-17
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26. Starter Questions Q1. True or false y ( y + 6 ) -7y = y2 -7y + 6
Credit
Q1. True or false
y ( y + 6 ) -7y = y2 -7y + 6
Q2. Fill in the ?
49 – 4x2 = ( ? + ?x)(? – 2?)
Q3. Write in scientific notation
31-Mar-17
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27. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
Learning Intention
Success Criteria
To show how to factorise trinomials ( quadratics) using
St. Andrew's Cross method.
Understand the steps of the St. Andrew’s Cross method.
2. Be able to factorise quadratics using SAC method.
31-Mar-17
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28. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
There are various ways of factorising
trinomials (quadratics)
e.g. The ABC method, FOIL method.
We will use the
St. Andrew’s cross method
to factorise trinomials / quadratics.
31-Mar-17
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29. Created by Mr. Lafferty@mathsrevision.com
Removing
Double Brackets
A LITTLE REVISION
Multiply out the brackets and Simplify
(x + 1)(x + 2)
1. Write down F O I L x2
+ 2x
+ x
+ 2
x2 + 3x + 2
2. Tidy up !
31-Mar-17
Created by Mr.

30. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method
We use the SAC method to go the opposite way
FOIL
(x + 1)(x + 2) x2
+ 3x
+ 2
SAC
(x + 1)(x + 2) x2
+ 3x
+ 2
31-Mar-17
Created by Mr.

31. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (+2)
and
Diagonals sum to give middle value +3x.
x2 + 3x + 2 x x
+ 2
+ 2
(+2) x( +1) = +2 x x
+ 1
+ 1
(+2x) +( +1x) = +3x
( ) ( )
31-Mar-17
Created by Mr.

32. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (+5)
and
Diagonals sum to give middle value +6x.
x2 + 6x + 5 x x
+ 5
+ 5
(+5) x( +1) = +5 x x
+ 1
+ 1
(+5x) +( +1x) = +6x
( ) ( )
31-Mar-17
Created by Mr.

33. Using St. Andrew’s Cross method
One number must be +
and one -
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (-12)
and
Diagonals sum to give middle value +x.
x2 + x - 12 x x
+ 4
+ 4
(+4) x( -3) = -12 x x
- 3
- 3
(+4x) +( -3x) = +x
( ) ( )
31-Mar-17
Created by Mr.

34. Using St. Andrew’s Cross method
Both numbers must be -
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (+4)
and
Diagonals sum to give middle value -4x.
x2 - 4x + 4 x x
- 2
- 2
(-2) x( -2) = +4 x x
- 2
- 2
(-2x) +( -2x) = -4x
( ) ( )
31-Mar-17
Created by Mr.

35. Using St. Andrew’s Cross method
One number must be +
and one -
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (-3)
and
Diagonals sum to give middle value -2x
x2 - 2x - 3 x x
- 3
- 3
(-3) x( +1) = -3 x x
+ 1
+ 1
(-3x) +( x) = -2x
( ) ( )
31-Mar-17
Created by Mr.

36. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
Factorise using SAC method
(m + 1 )( m + 1 )
(a) m2 + 2m + 1
y2 + 6y + 5
b2 – b - 2
(d) a2 – 5a + 6
( y + 5 )( y + 1 )
( b - 2 )( b + 1 )
( a - 3 )( a – 2 )
31-Mar-17
Created by Mr. Lafferty

37. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
Now try Ex6.1
Ch5 (page 93)
31-Mar-17
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38. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S3
Credit
Q1. Cash price for a sofa is £700.
HP terms are 10% deposit the 6 months equal payments of £120.
Show that you pay £90 using HP terms.
Q2. Factorise x – x2
31-Mar-17
Created by Mr.

39. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
Learning Intention
Success Criteria
To show how to factorise trinomials ( quadratics) of the form ax2 + bx +c using SAC.
Be able to factorise trinomials / quadratics using SAC.
31-Mar-17
Created by Mr.

40. Using St. Andrew’s Cross method
One number must be +
and one -
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (-4)
and
Diagonals sum to give middle value -x
3x2 - x - 4 3x 3x
- 4
- 4
(-4) x( +1) = -4 x x
+ 1
+ 1
(3x) +( -4x) = -x
( ) ( )
31-Mar-17
Created by Mr.

41. Using St. Andrew’s Cross method
One number must be +
and one -
Factorising
Using St. Andrew’s Cross method
Strategy for factorising quadratics
Find two numbers that
multiply to give last number (-3)
and
Diagonals sum to give middle value -x
2x2 - x - 3 2x 2x
- 3
- 3
(-3) x( +1) = -3 x x
+ 1
+ 1
(-3x) +( +2x) = -x
( ) ( )
31-Mar-17
Created by Mr.

42. Using St. Andrew’s Cross method
one number is + and
one number is -
Factorising
Using St. Andrew’s Cross method
Two numbers that multiply to give
last number (-3)
and
Diagonals sum to give middle value (-4x)
4x2 - 4x - 3 4x
Keeping the LHS fixed
Factors
1 and -3
-1 and 3 x
Can we do it !
( ) ( )
31-Mar-17
Created by Mr.

43. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method
Find another set of
factors for LHS
4x2 - 4x - 3
Repeat the factors for RHS to see if it factorises now 2x 2x
- 3
- 3
Factors
1 and -3
-1 and 3 2x 2x
+ 1
+ 1
( ) ( )
31-Mar-17
Created by Mr.

44. Using St. Andrew’s Cross method
Both numbers must be +
Factorising
Using St. Andrew’s Cross method
Find two numbers that
multiply to give last number (+15)
and
Diagonals sum to give middle value (+22x)
8x2+22x+15 8x
Keeping the LHS fixed
Factors
1 and 15
3 and 5
Find all the factors
of (+15) then try and factorise x
Can we do it !
( ) ( )
31-Mar-17
Created by Mr.

45. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method
Find another set of
factors for LHS
8x2+22x+15
Repeat the factors for RHS to see if it factorises now 4x 4x
+ 5
+ 5
Factors
3 and 5
1 and 15 2x 2x
+ 3
+ 3
( ) ( )
31-Mar-17
Created by Mr.

46. Using St. Andrew’s Cross method
Factorising
Using St. Andrew’s Cross method S3
Credit
Now try Ex 7.1
First 2 columns only
Ch5 (page 95)
31-Mar-17
Created by Mr.

47. Starter Questions S3
Credit
Use a multiplication table to expand out (2x – 5)(x + 5)
Q1.
Q2. After a 20% discount a watch is on sale
for £240.
What was the original price of the watch.
Q3. True or false 3a2 b – ab2 =a2b2(3b – a)
31-Mar-17
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48. Created by Mr. Lafferty@www.mathsrevision.com
Summary of
Factorising S3
Credit
Learning Intention
Success Criteria
To explain the factorising priorities.
Be able use the factorise priorities to factorise various expressions.
31-Mar-17
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49. Created by Mr. Lafferty@www.mathsrevision.com
Summary of
Factorising S3
Credit
When we are asked to factorise there is priority we
must do it in.
Take any common factors out and put them
outside the brackets.
2. Check for the difference of two squares.
3. Factorise any quadratic expression left.
31-Mar-17
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50. 2 Summary of Factorising www.mathsrevision.com squares
Credit
St. Andrew’s Cross method 2
squares
Difference
Take Out Common Factor
31-Mar-17
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51. Created by Mr. Lafferty@www.mathsrevision.com
If you can successfully complete this exercise then you have the necessary skills to pass the algebraic part of the course.
Summary of
Factorising S3
Credit
Now try Ex 8.1
Ch5 (page 97)
31-Mar-17
Created by Mr.