Algebra
Simplifying Algebraic Expressions
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Removing Brackets
Removing Brackets & Simplifying
Evaluating Expressions
Factorising – The common factor
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
1. A TV has been reduced in the sale
by 20%. It was £250. How much is it now.
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2. Simplify the ratio 16 : 64
3. 30% of £300
4. Tidy up the expression
2cm 3cm
5y + 3d + 4d + 10y
6cm 2cm
5. Find the area and perimeter of the shape.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Simplifying Algebraic Expressions
Learning Intention Success Criteria
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1. To review tidying up 1. To remember the phrase
expressions. ‘ like terms.’
2. To be able to simplify
simple algebraic expressions
by collecting ‘ like terms.’
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Simplifying Algebraic Expressions
Reminder !
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We can only add and subtract “ like terms “
x x x x 4x
9p 7p 2p
3a b a 6b 2a 7b
10 6w 1 9 6w
x x x 3x
2 2 2 2
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Simplifying Algebraic Expressions
Reminder !
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Multiplying terms
7 a 7a
w 5 5w
bb b
2 ( NOT 2b )
2m 4m 8m ( NOT 8m )
2
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Simplifying Algebraic Expressions
Question : Find the area of each of the 3 sections of this shape.
What is the total area.
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y 1 2 3
A3 2 y 2 y
2 y 2
A1 2 y 2 y A2 y y y 2
AT y 2 y 2 y y 4 y
2 2
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Simplifying Algebraic Expressions
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Now try Exercise 1
Ch11 (page 46)
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
1. Find the perimeter and area of the shape.
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2a
6h
2. Calculate (a) (-3m) x (-4m) (b) (2b) x (3a)
3. Find all the missing angles.
o
100
o
60
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Removing brackets
Learning Intention Success Criteria
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1. To explain how to multiply 1. Understand the key steps in
out simply algebraic removing brackets.
brackets.
2. Apply multiplication rules
for integers numbers when
removing brackets.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Removing a
Single Bracket
Example 1
3(b + 5) = 3b + 15
Example 2
4(w - 2) = 4w - 8
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 3
2(y - 1) = 2y - 2
Example 4
7(w - 6) = 7w - 42
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 5
8(x + 3) = 8x + 24
Example 6
4(3 -2m) = 12 - 8m
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 7 : Write down an expression
for the amount indicate below
in two difference ways.
x+3
x+3 3(x + 3) =3x + 9
x+3
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 8 : Write down an expression
for the amount indicate below
y-2 in two difference ways.
y-2 y-2
5(y - 2) = 5y - 10
y-2
y-2
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Algebra
Removing brackets
Question : Find the area of the rectangle
(i) With brackets
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(ii) Without brackets.
4
Y+5
(i) A 4( y 5)
(ii) A 4( y 5) 4 y 20
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Removing brackets
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Now try Exercise 2
Ch11 (page 48)
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
1. My shape has 2 pairs of parallel lines
and equal angles and lengths.
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What is my shape?
1 1
2. Calculate of
2 4
3. Remove brackets 4(5d - 6)
(x+2)cm
4. Calculate the area of the rectangle.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
7cm
Algebra
Removing Brackets & Simplifying
Learning Intention Success Criteria
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1. Understand how to remove
1. Explain how to remove
brackets
brackets and simplify.
2. Apply rules integer numbers.
3. Tidy up after removing
brackets.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Removing a
Single Bracket
Example 1
a(b + 5) = ab + 5a
Example 2
p(w - 2) = pw - 2p
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 3
y(y - 1) = y2 - y
Example 4
7w(w - 3) = 7w2 - 21w
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 5
a(a2 + 3b) = a3 + 3ab
Example 6
y2(3y -2c) = 3y3 - 2cy2
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 7
-(x + y) = -x - y
Example 8
-5(a - 7) = -5a + 35
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Tidy Up
Example 9
7 + 3(4 - y) = 7 + 12 - 3y
= 19 - 3y
Tidy Up
Example 10
9 - 3(8 - y) = 9 - 24 + 3y
23-Nov-11
= -15 + 3y
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Removing a
Single Bracket
Example 11
12 10
x Find my Area Find my Area (x - 2)
A = LxB A = LxB
A = 12x A = 10(x – 2)
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing a
Single Bracket
Example 12 : Find area of the orange border
12
10 Area =Big Rec – Small Rec
x (x - 2) = 12x – 10(x - 2)
= 12x – 10x + 20
= 2x + 20
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing Two Single Brackets
Tidy Up
Example 13
4(m - 3) - (m + 2) = 4m - 12 - m - 2
= 3m - 14
Tidy Up
Example 14
7(y - 1) - 2(y + 4) = 7y - 7 - 2y - 8
= 5y - 15
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing Two Single Brackets
Example 15 : Find an expression for the difference in
the areas.
(y - 5)
7 A = 7(y- 4) A = 4(y – 5) 4
(y- 4)
Difference = 7(y - 4) - 4(y – 5)
Calculate
3 x 14 – 8 = 7y - 28 - 4y + 20
difference if
= 34 = 3y - 8
y = 14
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Removing Two Single Brackets
Example 16 : Find an expression for the difference in
the areas.
(x + 1)
9 A = 9(x + 3) A = 7(x + 1) 7
x+3
Difference = 9(x + 3) - 7(x + 1)
Calculate
2 x 4 + 20 = 9x + 27 – 7x - 7
difference if
=28 = 2x + 20
x=4
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Algebra
Removing Brackets & Simplifying
Question : Find the area of the large rectangle, then the small
rectangle and hence find the area of the red section.
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x
x-3
6 4
AL 6 x AS 4( x 3) 4 x 12
AR 6 x (4 x 12) 2 x 12
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Removing Brackets & Simplifying
www.mathsrevision.com
Now try Exercise 3
Ch11 (page 50)
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
1. My shape has 2 pairs of parallel lines
equal lengths and opposite angles are equal.
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What is my shape?
1 1
2. Calculate of
3 4
3. Remove brackets and simplify 4e - (8e - 12)
(x+2)cm
4. Calculate the perimeter of the rectangle.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
7cm
Algebra
Evaluating Expressions – number for letter
Learning Intention Success Criteria
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1. Be able to substitute
1. To show how to evaluate
numbers for letters in an
an expression given values
expression.
for the letters.
2. Use previous knowledge to
evaluate expression.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Evaluating Expressions – number for letter
Given the following information find the values of :-
BODMAS
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a = 3 ; b = 4 and c = -1
5a 5 3 15
2a c 2 3 (1) 5
b a (4 4) (3 3) 16 9 7
2 2
2b 2 b b 2 4 4 32
2
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Evaluating Expressions – number for letter
Given the following information find the values of :-
a = 3 ; b = 4 and c = -1
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5c 5 c c 5 (1) (1) 5
2
2a 3b 30c
2
(2 a a) (3 b) (30 c)
(2 3 3) (3 4) (30 (1))
18 12 30 0
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Evaluating Expressions – number for letter
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Now try Exercise 4
Ch2 (page 51)
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
1. My shape has 1 line of symmetry, 1 pair of equal
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angles and adjcent lengths are equal.
What is my shape?
2. Find the highest common factor for
(a) 12 and 24 (b) 2x and 10x
3. Calculate 6a + 5ab when a = (-1) b = (-2)
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Factorising – The Common Factor
Learning Intention Success Criteria
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1. Be able to recognise the
1. To show how to reverse
HCF for set of values.
the process of removing
bracket ‘factorising’. 2. Understand the term
factorising.
3. Factorise simple expressions.
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Factorising by multiplying
Check
S3
out the bracket to get
Credit back to where you
Example Factorise 3x +started
15
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1. Find the HCF for 3x and 15 3
2. HCF goes outside the bracket 3( )
3. To see what goes inside the bracket
divide each term by HCF
3x ÷ 3 = x 15 ÷ 3 = 5 3( x + 5 )
23-Nov-11 Created by Mr. Lafferty@www.mathsrevision.com
Factorising by multiplying
Check
S3
out the bracket to get
Credit back to where you
started
Factorise 4x2 – 6xy
Example
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1. Find the HCF for 4x2 and 6xy 2x
2. HCF goes outside the bracket 2x( )
3. To see what goes inside the bracket
divide each term by HCF
4x2 ÷ 2x =2x 6xy ÷ 2x = 3y 2x( 2x- 3y )
23-Nov-11 Created by Mr. Lafferty@www.mathsrevision.com
Algebra
Factorising – The Common Factor
Simply find the HCF for a given set of data
and write the data using brackets :-
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HCF ?
6
6 x 12 6(x 2 )
HCF ?
4
8a 12b 4( 2a 3b )
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Algebra
Factorising – The Common Factor
Simply find the HCF for a given set of data
and write the data using brackets :-
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HCF ?
a
am an a(m n )
HCF ?
3x
9 x 6 x 3x( 3 2x )
2
23-Nov-11 Created by Mr. Lafferty Maths Dept.
Factorising
S3
Credit
Factorise the following :
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(a) 3x + 6 3(x + 2)
Be
(b) 4xy – 2x careful ! 2x(2y – 1)
(c) 6a + 7a2 a(6 + 7a)
(d) y2 - y y(y – 1)
23-Nov-11 Created by Mr. Lafferty@mathsrevision.com
Algebra
Factorising – The Common Factor
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Now try Exercise 5
Ch11 (page 54)
23-Nov-11 Created by Mr. Lafferty Maths Dept.