Algebra

1
Algebra
Simplifying Algebraic Expressions
Removing Brackets
Removing Brackets Simplifying
www.mathsrevision.com
Evaluating Expressions
Factorising The common factor
2
Starter Questions
www.mathsrevision.com
2cm
3cm
6cm
2cm
3
Algebra
Simplifying Algebraic Expressions
Learning Intention
Success Criteria

• To remember the phrase
• like terms.

• To review tidying up
• expressions.

2. To be able to simplify simple algebraic
expressions by collecting like terms.
www.mathsrevision.com
4
Algebra
Simplifying Algebraic Expressions
Reminder !
We can only add and subtract like terms
www.mathsrevision.com
5
Algebra
Simplifying Algebraic Expressions
Reminder !
Multiplying terms
www.mathsrevision.com
( NOT 2b )
( NOT 8m )
6
Algebra
Simplifying Algebraic Expressions
Question Find the area of each of the 3
sections of this shape. What is
the total area.
y
www.mathsrevision.com
y
2
2
7
Algebra
Simplifying Algebraic Expressions
Now try Exercise 1 Ch11 (page 46)
www.mathsrevision.com
8
Starter Questions
2a
6h
www.mathsrevision.com
9
Algebra
Removing brackets
Learning Intention
Success Criteria

1. Understand the key steps in removing brackets.

1. To explain how to multiply out simply
algebraic brackets.
2. Apply multiplication rules for integers
numbers when removing brackets.
www.mathsrevision.com
10
Removing a Single Bracket
Example 1
15
3(b 5)
3b
Example 2
- 8
4(w - 2)
4w
11
Removing a Single Bracket
Example 3
- 2
2(y - 1)
2y
Example 4
- 42
7(w - 6)
7w
12
Removing a Single Bracket
Example 5
24
8(x 3)
8x
Example 6
- 8m
4(3 -2m)
12
13
Removing a Single Bracket
Example 7 Write down an expression for the
amount indicate below in two difference ways.
x3
x3
9
3(x 3)
3x
x3
14
Removing a Single Bracket
Example 8 Write down an expression for the
amount indicate below in two difference ways.
y-2
y-2
y-2
- 10
5(y - 2)
5y
y-2
y-2
25-Dec-20
Created by Mr. Lafferty_at_mathsrevision.com
15
Algebra
Removing brackets
Question Find the area of the rectangle (i)
With brackets (ii) Without brackets.
4
www.mathsrevision.com
Y 5
16
Algebra
Removing brackets
Now try Exercise 2 Ch11 (page 48)
www.mathsrevision.com
17
Starter Questions
www.mathsrevision.com
(x2)cm
7cm
18
Algebra
Removing Brackets Simplifying
Learning Intention
Success Criteria
1. Understand how to remove brackets
1. Explain how to remove brackets and simplify.
2. Apply rules integer numbers.
www.mathsrevision.com
3. Tidy up after removing brackets.
19
Removing a Single Bracket
Example 1
5a
a(b 5)
ab
Example 2
- 2p
p(w - 2)
pw
20
Removing a Single Bracket
Example 3
- y
y(y - 1)
y2
Example 4
- 21w
7w(w - 3)
7w2
21
Removing a Single Bracket
Example 5
3ab
a(a2 3b)
a3
Example 6
- 2cy2
y2(3y -2c)
3y3
22
Removing a Single Bracket
Example 7
- y
-(x y)
-x
Example 8
35
-5(a - 7)
-5a
23
Removing a Single Bracket
Tidy Up
Example 9
- 3y
12
7 3(4 - y)
7
19 - 3y
Tidy Up
Example 10
- 24
3y
9 - 3(8 - y)
9
-15 3y
24
Removing a Single Bracket
Example 11
12
10
Find my Area
Find my Area
x
(x - 2)
A L x B
A L x B
A 10(x 2)
A 12x
25
Removing a Single Bracket
Example 12 Find area of the orange border
12
Area Big Rec Small Rec
10
x
(x - 2)
12x 10(x - 2)
12x 10x 20
2x 20
26
Removing Two Single Brackets
Tidy Up
Example 13
- m - 2
4(m - 3) - (m 2)
4m - 12
3m - 14
Tidy Up
Example 14
- 2y - 8
7(y - 1) - 2(y 4)
7y - 7
5y - 15
27
Removing Two Single Brackets
Example 15 Find an expression for the
difference in the areas.
(y - 5)
A 4(y 5)
4
7
A 7(y- 4)
(y- 4)
Calculate difference if y 14
3 x 14 8 34
Difference 7(y - 4) - 4(y 5)
7y - 28 - 4y 20
3y - 8
28
Removing Two Single Brackets
Example 16 Find an expression for the
difference in the areas.
(x 1)
A 7(x 1)
7
9
A 9(x 3)
x 3
Calculate difference if x 4
2 x 4 20 28
Difference 9(x 3) - 7(x 1)
9x 27 7x - 7
2x 20
29
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.
x
x-3
4
6
www.mathsrevision.com
30
Algebra
Removing Brackets Simplifying
Now try Exercise 3 Ch11 (page 50)
www.mathsrevision.com
31
Starter Questions
www.mathsrevision.com
(x2)cm
7cm
32
Algebra
Evaluating Expressions number for letter
Learning Intention
Success Criteria
1. Be able to substitute numbers for letters in
an expression.
1. To show how to evaluate an expression given
values for the letters.
2. Use previous knowledge to evaluate expression.
www.mathsrevision.com
33
Algebra
Evaluating Expressions number for letter
BODMAS
Given the following information find the values
of -
a 3 b 4 and c -1
www.mathsrevision.com
34
Algebra
Evaluating Expressions number for letter
Given the following information find the values
of -
a 3 b 4 and c -1
www.mathsrevision.com
35
Algebra
Evaluating Expressions number for letter
Now try Exercise 4 Ch2 (page 51)
www.mathsrevision.com
36
Starter Questions
www.mathsrevision.com
37
Algebra
Factorising The Common Factor
Learning Intention
Success Criteria
1. Be able to recognise the HCF for set of
values.
1. To show how to reverse the process of
removing bracket factorising.
2. Understand the term factorising.
www.mathsrevision.com
3. Factorise simple expressions.
38
Check by multiplying out the bracket to get back
to where you started
Factorising
S3 Credit
Factorise 3x 15
Example
1. Find the HCF for 3x and 15
3
2. HCF goes outside the bracket
3( )
www.mathsrevision.com

• To see what goes inside the bracket
• divide each term by HCF

3x 3 x
15 3 5
3( x 5 )
39
Check by multiplying out the bracket to get back
to where you started
Factorising
S3 Credit
Factorise 4x2 6xy
Example
1. Find the HCF for 4x2 and 6xy
2x
2. HCF goes outside the bracket
2x( )
www.mathsrevision.com

• To see what goes inside the bracket
• divide each term by HCF

4x2 2x 2x
6xy 2x 3y
2x( 2x- 3y )
40
Algebra
Factorising The Common Factor
Simply find the HCF for a given set of data and
write the data using brackets -
HCF ?
6
www.mathsrevision.com
HCF ?
4
41
Algebra
Factorising The Common Factor
Simply find the HCF for a given set of data and
write the data using brackets -
HCF ?
a
www.mathsrevision.com
HCF ?
3x
42
Factorising
S3 Credit
Factorise the following
3(x 2)

• (a) 3x 6
• 4xy 2x
• 6a 7a2
• (d) y2 - y

Be careful !
2x(2y 1)
www.mathsrevision.com
a(6 7a)
y(y 1)
43
Algebra
Factorising The Common Factor
Now try Exercise 5 Ch11 (page 54)
www.mathsrevision.com