Algebra www.mathsrevision.com
S4
Removing Brackets & Simplifying Factors Simple Factorising 28-Apr-13
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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.
28-Apr-13
Created by Mr. Lafferty Maths Dept.
2cm
Algebra
Removing Brackets & Simplifying
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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.
28-Apr-13
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 28-Apr-13
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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 28-Apr-13
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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 28-Apr-13
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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 28-Apr-13
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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 !
=-4 28-Apr-13
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Removing a Single Bracket
S4
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Example 7
a(y - 1) = ay - a Example 8
p(w - 6) = pw - 6p 28-Apr-13
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Removing a Single Bracket
S4
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Example 9
x(x + 3) = x2 + 3x Example 10
3q(3q -2m) = 9q2 - 6mq 28-Apr-13
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Algebra
Removing Brackets & Simplifying
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S4
Now try Ex 1 Ch15 (page 172)
28-Apr-13
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. 28-Apr-13
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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
28-Apr-13
Success Criteria 1. To identify factors using factor pairs 2. Find HCF for two numbers by comparing factors.
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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
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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. 28-Apr-13
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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 28-Apr-13
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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
28-Apr-13
F10x = 1, and 10x 2 and 5x HCF = 5 5 and 2x Created by Mr.
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Factors www.mathsrevision.com
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
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Factors www.mathsrevision.com
S4
Now try Ex 2 Ch15 (page 173)
28-Apr-13
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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 28-Apr-13
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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.
28-Apr-13
Success Criteria 1. To identify the HCF for given terms. 2. Factorise terms using the HCF and one bracket term.
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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
28-Apr-13
15 ÷ 3 = 5 Created by Mr.
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3 3(
)
3( x + 5 )
Check by multiplying Factorising
out the bracket to get back to where you 2 started
S4
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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
28-Apr-13
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
28-Apr-13
3(x + 2)
3x + 6 Be careful !
2x(2y – 1) a(6 + 7a)
-xy + 4x
x(y2 – y + 4)
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Factorising www.mathsrevision.com
S4
Now try Ex 3 Ch15 (page 175)
28-Apr-13
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