Algebra

1
Algebra
S4
Removing Brackets Simplifying
Factors
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Simple Factorising
2
Starter Questions
S4
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2cm
3cm
6cm
2cm
3
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.
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3. Tidy up after removing brackets.
4
Removing a Single Bracket
Example 1
15
3(b 5)
3b
Example 2
- 8
4(w - 2)
4w
5
Be careful with negatives !!
Removing a Single Bracket
Example 3
- 10
-2(h 5)
-2h
Example 4
9
-(g - 9)
-g
6
Be careful only multiply everything inside the
bracket
Removing a Single Bracket
Example 4
8 2(h 3)
8
6
2h
Now tidy up !
14
2h
7
Be careful only multiply everything inside the
bracket
Removing a Single Bracket
Example 5
-2(y - 1) 4
-2y
4
2
Now tidy up !
6
-2y
8
Be careful only multiply everything inside the
bracket
Removing a Single Bracket
Example 6
y - (4 - y)
y
y
- 4
Now tidy up !
2y - 4
9
Removing a Single Bracket
Example 7
- a
a(y - 1)
ay
Example 8
- 6p
p(w - 6)
pw
10
Removing a Single Bracket
Example 9
3x
x(x 3)
x2
Example 10
- 6mq
3q(3q -2m)
9q2
11
Algebra
Removing Brackets Simplifying
S4
Now try Ex 1 Ch15 (page 172)
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12
Starter Questions
S4
Q1. Multiply out (a) a (6h 3x)
Q2. True or false
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Q3. Write down all the number that divide into
12 without leaving a remainder.
13
Factors
Using Factors
S4
Learning Intention
Success Criteria

1. To identify factors using factor pairs

1. To explain that a factor divides into a number
   without leaving a remainder
2. To explain how to find Highest Common Factors

1. Find HCF for two numbers by comparing factors.

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14
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
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4 and 14
7 and 8
15
Factors
Highest Common Factor
S4
Highest Common Factor
Largest Same Number
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We need to write out all factor pairs in order to
find the Highest Common Factor.
16
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
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HCF 4
17
Factors
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
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HCF b
18
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
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Example Find the HCF of 5 and 10x.
F5 1 and 5
F10x 1, and 10x
2 and 5x
HCF 5
5 and 2x
10 and x
19
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
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4h
ab
20
Factors
S4
Now try Ex 2 Ch15 (page 173)
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21
Starter Questions
S4
Q1. Expand out a (4y 3x) -2y
Q2. Write out in full
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Q3. True or False all the factors of 5x2 are 1,
x, 5
22
Factorising
Using Factors
S4
Learning Intention
Success Criteria

1. To identify the HCF for given terms.

1. To show how to factorise terms using the Highest
   Common Factor and one bracket term.

1. Factorise terms using the HCF and one bracket
   term.

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23
Check by multiplying out the bracket to get back
to where you started
Factorising
S4
Factorise 3x 15
Example
1. Find the HCF for 3x and 15
3
2. HCF goes outside the bracket
3( )
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• To see what goes inside the bracket
• divide each term by HCF

3x 3 x
15 3 5
3( x 5 )
24
Check by multiplying out the bracket to get back
to where you started
Factorising
S4
Factorise 2x2 4xy 6
Example
1. Find the HCF for 2x2, 4xy and 6
2
2. HCF goes outside the bracket
2( )
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• To see what goes inside the bracket
• divide each term by HCF

2x2 2 x2
6 2 3
2(x2- 2xy 3)
4xy 2 2xy
25
Factorising
S4
Factorise the following
3(x 2)

• (a) 3x 6
• 4xy 2x
• 6a 7a2
• (d) xy2 -xy 4x

Be careful !
2x(2y 1)
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a(6 7a)
x(y2 y 4)
26
Factorising
S4
Now try Ex 3 Ch15 (page 175)
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