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Algebra
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S4
Removing Brackets & Simplifying
Factors
Simple Factorising
13-May-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
S4
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1. A TV has be reduced in the sale
by 20%. It was £250. How much is it now.
2.
5% of 300p
3.
Tidy up the expression
5y + 3d + 4d + 10y
4.
2cm
3cm
6cm
Find the area and perimeter of the shape.
13-May-17
Created by Mr. Lafferty Maths Dept.
2cm
Algebra
Removing Brackets & Simplifying
www.mathsrevision.com
S4
Learning Intention
1. Explain how to remove
brackets and simplify.
Success Criteria
1. Understand how to remove
brackets
2. Apply rules integer numbers.
3. Tidy up after removing
brackets.
13-May-17
Created by Mr. Lafferty Maths Dept.
Removing a
Single Bracket
S4
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Example 1
3(b + 5) = 3b + 15
Example 2
4(w - 2) = 4w - 8
13-May-17
Created by Mr. [email protected]
Removing a Be careful
with
Single Bracketnegatives
!!
S4
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Example 3
-2(h + 5) = -2h - 10
Example 4
-(g - 9) = -g + 9
13-May-17
Created by Mr. [email protected]
Removing a
Single Bracket
Be careful
only multiply
everything inside
the bracket
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S4
Example 4
8 +2(h + 3) = 8 + 2h + 6
Now tidy up !
= 2h + 14
13-May-17
Created by Mr. [email protected]
Removing a
Single Bracket
Be careful
only multiply
everything inside
the bracket
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S4
Example 5
-2(y - 1) + 4 = -2y + 2 + 4
Now tidy up !
= -2y + 6
13-May-17
Created by Mr. [email protected]
Removing a
Single Bracket
Be careful
only multiply
everything inside
the bracket
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S4
Example 6
y - (4 - y) = y - 4 + y
Now tidy up !
= 2y - 4
13-May-17
Created by Mr. [email protected]
Removing a
Single Bracket
S4
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Example 7
a(y - 1) = ay - a
Example 8
p(w - 6) = pw - 6p
13-May-17
Created by Mr. [email protected]
Removing a
Single Bracket
S4
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Example 9
x(x + 3) = x2 + 3x
Example 10
3q(3q -2m) = 9q2 - 6mq
13-May-17
Created by Mr. [email protected]
Algebra
Removing Brackets & Simplifying
www.mathsrevision.com
S4
Now try Ex 1
Ch15 (page 172)
13-May-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
S4
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Q1.
Multiply out
(a)
a (6h – 3x)
Q2. True or false
5 1 4
1
  1
6 3 3
3
Q3. Write down all the number that divide
into 12 without leaving a remainder.
13-May-17
Created by Mr. [email protected]
Factors
Using Factors
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S4
Learning Intention
1. To explain that a factor
divides into a number
without leaving a
remainder
2. To explain how to find
Highest Common Factors
13-May-17
Success Criteria
1. To identify factors using
factor pairs
2. Find HCF for two numbers
by comparing factors.
Created by Mr. [email protected]
Factors
Factors
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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
13-May-17
8
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Factors
Highest Common Factor
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S4
Highest
Common
Factor
Largest
Same
Number
We need to write out all factor pairs in order
to find
the Highest Common Factor.
13-May-17
Created by Mr. [email protected]
Factors
Highest Common Factor
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S4
Example :Find the HCF of 8 and 12.
F8 = 1 and 8
F12 =
2 and 4
1 and 12
2 and 6
3 and 4
HCF = 4
13-May-17
Created by Mr. [email protected]
Factors
Highest Common Factor
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S4
Example :
F ab =
Find the HCF of ab and 2b.
1 and ab F2b =
a and b
1 and 2b
2 and
HCF = b
b
Factors
Highest Common Factor
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S4
Example :
Find the HCF of 4x and x2.
F4x = 1, and 4x
2 and 2x
4 and
Example :
Fx2 = 1 and x2
x and x
x
HCF = x
Find the HCF of 5 and 10x.
F5 = 1 and 5
13-May-17
F10x = 1, and 10x
2 and 5x
HCF = 5
5 and 2x
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10 and x
Factors
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S4
Find the HCF for these terms
(a)
16w and 24w
8w
(b) 9y2 and 6y
3y
(c)
4h and 12h2
4h
(d) ab2 and a2b
ab
13-May-17
Created by Mr. [email protected]
Factors
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S4
Now try Ex 2
Ch15 (page 173)
13-May-17
Created by Mr. Lafferty
Starter Questions
S4
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Q1.
Expand out
a (4y – 3x) -2y
Q2. Write out in full
4.85 10
3
Q3. True or False all the factors of 5x2 are
1, x, 5
13-May-17
Created by Mr. [email protected]
Factorising
Using Factors
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S4
Learning Intention
1. To show how to factorise
terms using the Highest
Common Factor and one
bracket term.
13-May-17
Success Criteria
1. To identify the HCF for
given terms.
2. Factorise terms using the
HCF and one bracket term.
Created by Mr. [email protected]
Check by multiplying
Factorising
S4
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Example
out the bracket to get
back to where you
Factorise 3x +started
15
1.
Find the HCF for 3x and 15
2.
HCF goes outside the bracket
3.
To see what goes inside the bracket
divide each term by HCF
3x ÷ 3 = x
13-May-17
15 ÷ 3 = 5
Created by Mr. [email protected]
3
3(
)
3( x + 5 )
Check by multiplying
Factorising
out the bracket to get
back to where you
2 started
S4
www.mathsrevision.com
Example
Factorise 2x – 4xy + 6
1.
Find the HCF for 2x2, 4xy and 6
2.
HCF goes outside the bracket
3.
To see what goes inside the bracket
divide each term by HCF
2x2 ÷ 2 = x2
6÷2=3
4xy ÷ 2 = 2xy
13-May-17
2(
2
)
2(x2- 2xy +3)
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Factorising
S4
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Factorise the following :
(a)
(b)
4xy – 2x
(c)
6a + 7a2
(d)
xy2
13-May-17
3(x + 2)
3x + 6
Be
careful !
2x(2y – 1)
a(6 + 7a)
-xy + 4x
x(y2 – y + 4)
Created by Mr. [email protected]
Factorising
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S4
Now try Ex 3
Ch15 (page 175)
13-May-17
Created by Mr. [email protected]