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### Algebra

Simplifying Algebraic Expressions

Removing Brackets

Removing Brackets & Simplifying

www.mathsrevision.com

Evaluating Expressions

Factorising – The common factor

Created by Mr. Lafferty Maths Dept.

Simplifying Algebraic Expressions

Learning Intention

Success Criteria

- To remember the phrase
- ‘ like terms.’

- To review tidying up
- expressions.

- 2. Understand and be able too simplify simple algebraic expressions by collecting ‘ like terms.’

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Reminder !

We can only add and subtract “ like terms “

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Multiply the numbers together

multiply the letters together.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Reminder !

Multiplying terms

www.mathsrevision.com

( NOT 2b )

( NOT 8m )

Created by Mr. Lafferty Maths Dept.

2

3

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

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

2

y

2

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Now try Exercise 1

Ch11 (page 46)

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Removing brackets

Learning Intention

Success Criteria

- Understand the key steps in removing brackets.

- 1. We are learning how to multiply out simply algebraic brackets.

- 2. Apply multiplication rules for positive and negative numbers when removing brackets.

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 1

+ 15

3(b + 5) =

3b

Example 2

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- 8

4(w - 2) =

4w

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 3

- 2

2(y - 1) =

2y

Example 4

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- 42

7(w - 6) =

7w

Created by Mr. [email protected]evision.com

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 5

+ 24

8(x + 3) =

8x

Example 6

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- 8m

4(3 -2m) =

12

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 7 : Write down an expression

for the amount indicate below

in two difference ways.

x+3

x+3

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+ 9

3(x + 3)

=3x

x+3

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 8 : Write down an expression

for the amount indicate below

in two difference ways.

y-2

y-2

y-2

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- 10

5(y - 2)

= 5y

y-2

y-2

10-Mar-14

Created by Mr. [email protected]

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing brackets

Question : Find the area of the rectangle

(i) With brackets

(ii) Without brackets.

y + 5

(i) A = L x B

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4

= 4(y + 5)

(ii) = 4(y + 5)

= 4y

+ 20

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing brackets

Now try Exercise 2

Ch11 (page 48)

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Removing Brackets & Simplifying

Learning Intention

Success Criteria

1. Understand how to remove brackets

- 1. We are learning how to remove brackets and simplify.

2. Understand the need to show clear working.

www.mathsrevision.com

3. Apply to context questions.

Created by Mr. Lafferty Maths Dept.

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 1

+ 5a

a(b + 5) =

ab

Example 2

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- 2p

p(w - 2) =

pw

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 3

- y

y(y - 1) =

y2

Example 4

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- 21w

7w(w - 3) =

7w2

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 5

+ 3ab

a(a2 + 3b) =

a3

Example 6

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- 2cy2

y2(3y -2c) =

3y3

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 7

- y

-(x + y) =

-x

Example 8

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+ 35

-5(a - 7) =

-5a

Created by Mr. [email protected]

Single Bracket

Tidy Up

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 9

- 3y

12

7 + 3(4 - y) =

7 +

= 19 - 3y

Tidy Up

Example 10

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- 24

+ 3y

9 - 3(8 - y) =

9

= -15 + 3y

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 11

12

10

Find my Area

Find my Area

x

(x - 2)

www.mathsrevision.com

A = L x B

A = L x B

A = 10(x – 2)

A = 12x

Created by Mr. [email protected]

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 12 : Find area of the orange border

12

Area =Big Rec – Small Rec

10

x

(x - 2)

= 12x – 10(x - 2)

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= 12x

-10x

+ 20

= 2x + 20

Created by Mr. [email protected]

Tidy Up

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 13

- m - 2

4(m - 3) - (m + 2) =

4m - 12

= 3m - 14

Tidy Up

Example 14

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- 2y - 8

7(y - 1) - 2(y + 4) =

7y - 7

= 5y - 15

Created by Mr. [email protected]

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 15 : Find an expression for the difference in

the areas.

(y - 5)

A = 4(y – 5)

7

4

A = 7(y - 4)

www.mathsrevision.com

(y - 4)

Calculate difference if y = 14

Diff = 3 x 14 – 8

= 34

Difference = 7(y - 4) - 4(y – 5)

= 7y - 28

- 4y + 20

= 3y - 8

Created by Mr. [email protected]

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 16 : Find an expression for the difference in

the areas.

(x + 1)

A = 7(x + 1)

9

7

A = 9(x + 3)

www.mathsrevision.com

x + 3

Calculate difference if x = 4

Diff = 2 x 4 + 20

=28

Difference = 9(x + 3) - 7(x + 1)

= 9x + 27

– 7x - 7

= 2x + 20

Created by Mr. [email protected]

MTH 3-14a

MTH 4-14a

MTH 4-14b

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

Ab= 6x

6

www.mathsrevision.com

As= 4(x - 3)

= 4x

- 12

As= 6x - 4(x - 3)

= 6x

- 4x

+ 12

= 2x + 12

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing Brackets & Simplifying

Now try Exercise 3

Ch11 (page 50)

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Evaluating Expressions – number for letter

Learning Intention

Success Criteria

1. Be able to substitute numbers for letters in an expression.

- 1. We are learning how to evaluate an expression.

2. Use previous knowledge of Number to evaluate a expression.

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

BODMAS

Given the following information find the values of :-

a = 3 ; b = 4 and c = -1

2a + c

b2 – a2

2b2

= 42 – 32

= 2x3 + (-1)

= 2x(4)2

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= 16 – 9

= 2x3 - 1

= 2x16

= 6 - 1

= 7

= 32

= 5

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

Given the following information find the values of :-

a = 3 ; b = 4 and c = -1

2a2 + 3b + 30c

= 2x(3)2 + 3x4 + 30x(-1)

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= 18 + 12 - 30

= 0

Created by Mr. Lafferty Maths Dept.

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

Now try Exercise 4

Ch2 (page 51)

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Factorising – The Common Factor

Learning Intention

Success Criteria

1. Understand the term factorising.

- 1. We are learning the process of factorising’.

2. Apply previous knowledge to recognise the HCF for a set of values.

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3. Analysis answer to validate it is correct.

Created by Mr. Lafferty Maths Dept.

Check by multiplying out the bracket to get back to where you started

Factorising

MTH 3-14a

MTH 4-14a

MTH 4-14b

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

15

3x

3( x + 5 )

= x

= 5

3

3

Created by Mr. [email protected]

Check by multiplying out the bracket to get back to where you started

Factorising

MTH 3-14a

MTH 4-14a

MTH 4-14b

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

6xy

4x2

2x( 2x - 3y )

= 2x

= 3y

2x

2x

Created by Mr. [email protected]

Algebra you started

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Simply find the HCF for a given set of data

and write the data using brackets :-

8a – 12b

6x – 12

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= ( )

= ( )

4

2a

- 3b

6

x

- 2

Created by Mr. Lafferty Maths Dept.

Algebra you started

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Simply find the HCF for a given set of data

and write the data using brackets :-

9f – 6f2

am + an

www.mathsrevision.com

= ( )

= ( )

3f

3

- 2f

a

m

+ n

Created by Mr. Lafferty Maths Dept.

Factorising you started

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorise the following :

= ( )

3

x

+ 2

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

= ( )

2x

2y

- 1

www.mathsrevision.com

= ( )

a

6

+ 7a

= ( )

y

y

- 1

Created by Mr. [email protected]

Algebra you started

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Now try Exercise 5

Ch11 (page 54)

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

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