1. Created by Mr. Lafferty Maths Dept.
Algebra S4
Removing Brackets & Simplifying
Factors
Simple Factorising
14-Apr-17
Created by Mr. Lafferty Maths Dept.

2. Created by Mr. Lafferty Maths Dept.
Starter Questions S4
2cm
3cm
6cm
2cm
14-Apr-17
Created by Mr. Lafferty Maths Dept.

3. Created by Mr. Lafferty Maths Dept.
Algebra
Removing Brackets & Simplifying S4
Learning Intention
Success Criteria
1. Understand how to remove brackets
1. Explain how to remove brackets and simplify.
2. Apply rules integer numbers.
3. Tidy up after removing brackets.
14-Apr-17
Created by Mr. Lafferty Maths Dept.

4. Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 1
3(b + 5) = 3b
+ 15
Example 2
4(w - 2) = 4w
- 8
14-Apr-17
Created by Mr.

5. Removing a Single Bracket
Be careful with negatives !!
Removing a
Single Bracket
Example 3
-2(h + 5) =
-2h
- 10
Example 4
-(g - 9) = -g
+ 9
14-Apr-17
Created by Mr.

6. Removing a Single Bracket
Be careful
only multiply everything inside the bracket
Removing a
Single Bracket
Example 4
8 +2(h + 3) = 8
+ 2h
+ 6
Now tidy up !
= 2h
+ 14
14-Apr-17
Created by Mr.

7. Removing a Single Bracket
Be careful
only multiply everything inside the bracket
Removing a
Single Bracket
Example 5
-2(y - 1) + 4 =
-2y
+ 2
+ 4
Now tidy up !
= -2y
+ 6
14-Apr-17
Created by Mr.

8. Removing a Single Bracket
Be careful
only multiply everything inside the bracket
Removing a
Single Bracket
Example 6
y - (4 - y) = y
- 4
+ y
Now tidy up !
= 2y - 4
14-Apr-17
Created by Mr.

9. Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 7
a(y - 1) = ay
- a
Example 8
p(w - 6) = pw
- 6p
14-Apr-17
Created by Mr.

10. Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 9
x(x + 3) = x2
+ 3x
Example 10
3q(3q -2m) =
9q2
- 6mq
14-Apr-17
Created by Mr.

11. Created by Mr. Lafferty Maths Dept.
Algebra
Removing Brackets & Simplifying S4
Now try Ex 1
Ch15 (page 172)
14-Apr-17
Created by Mr. Lafferty Maths Dept.

12. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S4
Q1. Multiply out
(a) a (6h – 3x)
Q2. True or false
Q3. Write down all the number that divide
into 12 without leaving a remainder.
14-Apr-17
Created by Mr.

13. Created by Mr. Lafferty@mathsrevision.com
Factors
Using Factors S4
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.
14-Apr-17
Created by Mr.

14. Created by Mr. Lafferty@mathsrevision.com
Factors
Factors S4
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
14-Apr-17
Created by Mr.

15. Factors Highest Common Factor Largest Same Number
We need to write out all factor pairs in order to find
the Highest Common Factor.
14-Apr-17
Created by Mr.

16. Created by Mr. Lafferty@mathsrevision.com
Factors
Highest Common Factor S4
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
14-Apr-17
Created by Mr.

17. Factors F ab = 1 and ab F2b = 1 and 2b a and b 2 and b HCF = b
Highest Common Factor S4
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

18. Created by Mr. Lafferty@mathsrevision.com
Factors
Highest Common Factor S4
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
14-Apr-17
Created by Mr.
10 and x

19. Created by Mr. Lafferty@mathsrevision.com
Factors S4
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
14-Apr-17
Created by Mr.

20. Factors Now try Ex 2 Ch15 (page 173) www.mathsrevision.com S4
14-Apr-17
Created by Mr. Lafferty

21. Created by Mr. Lafferty@mathsrevision.com
Starter Questions S4
Q1. Expand out a (4y – 3x) -2y
Q2. Write out in full
Q3. True or False all the factors of 5x2 are
1, x, 5
14-Apr-17
Created by Mr.

22. Created by Mr. Lafferty@www.mathsrevision.com
Factorising
Using Factors S4
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.
14-Apr-17
Created by Mr.

23. 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 S4
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 )
14-Apr-17
Created by Mr.

24. Factorising 2(x2- 2xy +3) Example Factorise 2x2 – 4xy + 6
Check by multiplying out the bracket to get back to where you started
Factorising S4
Example
Factorise 2x2 – 4xy + 6
1. Find the HCF for 2x2, 4xy and 6 2
2. HCF goes outside the bracket
2( )
To see what goes inside the bracket
divide each term by HCF
2x2 ÷ 2 = x2
6 ÷ 2 = 3
4xy ÷ 2 = 2xy
2(x2- 2xy +3)
14-Apr-17
Created by Mr.

25. Created by Mr. Lafferty@mathsrevision.com
Factorising S4
Factorise the following :
3(x + 2)
(a) 3x + 6
4xy – 2x
6a + 7a2
(d) xy2 -xy + 4x
Be careful !
2x(2y – 1)
a(6 + 7a)
x(y2 – y + 4)
14-Apr-17
Created by Mr.

26. Created by Mr. Lafferty@www.mathsrevision.com
Factorising S4
Now try Ex 3
Ch15 (page 175)
14-Apr-17
Created by Mr.