8-aug-15created by mr. lafferty maths dept. simplifying algebraic expressions removing brackets...

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Simplifying Algebraic Expressions

Removing Brackets

AlgebraAlgebraw

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Removing Brackets & Simplifying

Evaluating Expressions

Factorising – The common factor


Starter QuestionsStarter Questionsw

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1. A TV has been reduced in the sale

by 20%. I t was £250. How much is it now.

3. 30% of £300

4. Tidy up the expression

5y + 3d +4d + 10y

5. Find the area and

2. Simplif y the ratio 16:64

perimeter of the shape.6cm

2cm

2cm

3cm

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1.1. To remember the To remember the phrase phrase

‘ ‘ like terms.’like terms.’

1. To review tidying up expressions.

AlgebraAlgebraSimplifying Algebraic Expressions

2.2. To be able to simplify To be able to simplify simple algebraic simple algebraic expressions by collecting ‘ expressions by collecting ‘ like terms.’like terms.’


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Reminder !We can only add and subtract “ like terms “

x x x x 4x9 7p p 2p

10 6 1w 3 6a b a b

2 2 2x x x

2 7a b9 6w

23x


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Reminder !Multiplying terms

7 a 7a5w 5w

2 4m m b b 2b

28m

( NOT 2b )

( NOT 8m )


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y 2

y

2

Question : Find the area of each of the 3 sections of this shape. What is the total area.

1 2A y 2A y y

3 2A y

2y

2y

2y

2 2 2TA y y y 2 4y y

1 2 3


Now try Exercise 1Ch11 (page 46)

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1. Find the perimeter and area of the shape.

3. Find all the missing angles.

2. Calculate (a) (-3m) x (-4m) (b) (2b) x (3a)

6h

2a

100o

60o


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1.1. Understand the key steps Understand the key steps in removing brackets.in removing brackets.

1. To explain how to multiply out simply algebraic brackets.

AlgebraAlgebra

2.2. Apply multiplication Apply multiplication rules rules for integers numbers for integers numbers when when removing brackets.removing brackets.

Removing brackets

3(b + 5) =3b + 15

Example 1

4(w - 2) =4w - 8

Example 2

Apr 19, 2023Apr 19, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

Removing aRemoving aSingle BracketSingle Bracket

2(y - 1) =2y - 2

Example 3

7(w - 6) =7w- 42

Example 4



8(x + 3) =8x+ 24

Example 5

4(3 -2m) = 12 - 8m

Example 6



Example 7 : Write down an expressionfor the amount indicate belowin two difference ways.

3(x + 3) =3x + 9



x+3

x+3

x+3

Example 8 : Write down an expressionfor the amount indicate belowin two difference ways.

5(y - 2) = 5y - 10



y-2

y-2 y-2

y-2y-2


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AlgebraAlgebra

Y + 5

4

Question : Find the area of the rectangle (i) With brackets(ii) Without brackets.

(i) 4( 5)A y

(ii) 4( 5)A y 4 20y

Removing brackets



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AlgebraAlgebra Removing brackets



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1. My shape has 2 pairs of parallel lines

and equal angles and lengths.

What is my shape?

1 12. Calculate of

2 4

3. Remove brackets 4(5d - 6)

4. Calculate the area of the rectangle.

7cm

(x+2)cm


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1. Explain how to remove brackets and simplify.

1. Understand how to remove brackets

AlgebraAlgebraRemoving Brackets & Simplifying

3. Tidy up after removing brackets.

2. Apply rules integer numbers.

a(b + 5) =ab + 5a

Example 1

p(w - 2) =pw - 2p

Example 2



y(y - 1) = y2 - y

Example 3

7w(w - 3) =7w2 - 21w

Example 4



a(a2 + 3b) =a3 + 3ab

Example 5

y2(3y -2c) =3y3 - 2cy2

Example 6



-(x + y) = -x - y

Example 7

-5(a - 7) =-5a + 35

Example 8



7 + 3(4 - y) =7 + 12

Example 9

9 - 3(8 - y) =9 - 24

Example 10



- 3y= 19 - 3y

Tidy Up

+ 3y

Tidy Up

= -15 + 3y

A = 10(x – 2)

Example 11



Find my Area (x - 2)

10

Find my Areax

12

A = 12x

A = L x B A = L x B

Example 12 : Find area of the orange border



(x - 2)10

x

12

Area =Big Rec – Small Rec

= 12x – 10(x - 2)

= 12x – 10x + 20

= 2x + 20

4(m - 3) - (m + 2) =4m - 12 - m - 2

Example 13

Example 14


= 3m - 14

Tidy Up

7(y - 1) - 2(y + 4) =7y - 7 - 2y - 8 = 5y - 15

Tidy Up

Removing Two Single Removing Two Single BracketsBrackets

3 x 14 – 8= 34

A = 4(y – 5)

Example 15 : Find an expression for the difference inthe areas.


(y - 5)

47 A = 7(y- 4)

(y- 4)Difference = 7(y - 4) - 4(y – 5)

= 7y - 28 - 4y + 20= 3y - 8

Calculate difference if

y = 14


2 x 4 + 20=28

A = 7(x + 1)

Example 16 : Find an expression for the difference inthe areas.


(x + 1)

79 A = 9(x + 3)

x + 3Difference = 9(x + 3) - 7(x + 1) = 9x + 27 – 7x - 7

= 2x + 20

Calculate difference if

x = 4



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AlgebraAlgebra

x

6

Question : Find the area of the large rectangle, then the small rectangle and hence find the area of the red section.

6LA x 4( 3)SA x 4 12x

4x-3

6 (4 12)RA x x 2 12x

Removing Brackets & Simplifying



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AlgebraAlgebraRemoving Brackets & Simplifying



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1. My shape has 2 pairs of parallel lines

equal lengths and opposite angles are equal.

What is my shape?

1 12. Calculate of

3 4

3. Remove brackets and simplif y 4e- (8e -12)

4. Calculate the perimeter of the rectangle.

7cm

(x+2)cm


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1. To show how to evaluate an expression given values for the letters.

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

AlgebraAlgebra

2. Use previous knowledge to evaluate expression.

Evaluating Expressions – number for letter


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AlgebraAlgebraEvaluating Expressions – number for letter

Given the following information find the values of :-

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

BODMAS

5 a 5 3 15 2a c 2 3 ( 1)

22b

2 2b a (4 4) (3 3)

2 4 4

516 9 7

2 b b 32


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Given the following information find the values of :-

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

25c 5 ( 1) ( 1) 5 c c 5

22 3 30a b c

(2 3 3) (3 4) (30 ( 1)) (2 ) (3 ) (30 )a a b c

18 12 30 0



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ww

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.com 1. My shape has 1 line of symmetry, 1 pair of equal

angles and adjcent lengths are equal.

What is my shape?

2. Find the highest common f actor f or

(a) 12 and 24 (b) 2x and 10x

3. Calculate 6a+ 5ab when a=(-1) b=(-2)


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1. To show how to reverse the process of removing bracket ‘factorising’.

1. Be able to recognise the HCF for set of values.

AlgebraAlgebra

2. Understand the term factorising.

Factorising – The Common Factor

3. Factorise simple expressions.

19 Apr 202319 Apr 2023 Created by Mr. [email protected] by Mr. [email protected]

FactorisingFactorisingw

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Example Factorise 3x + 15

1. Find the HCF for 3x and 15 3

2. HCF goes outside the bracket 3( )

3. To see what goes inside the bracketdivide each term by HCF

3x ÷ 3 = x 15 ÷ 3 = 5 3( x + 5 )

Check by multiplying out the bracket to get back to where

you started

S3 Credit

19 Apr 202319 Apr 2023 Created by Mr. [email protected] by Mr. [email protected]

FactorisingFactorisingw

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Example

1. Find the HCF for 4x2 and 6xy 2x

2. HCF goes outside the bracket 2x( )

3. To see what goes inside the bracketdivide each term by HCF

4x2 ÷ 2x =2x 6xy ÷ 2x = 3y 2x( 2x- 3y )

Factorise 4x2 – 6xy

Check by multiplying out the bracket to get back to where

you started

S3 Credit


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AlgebraAlgebra

Simply find the HCF for a given set of data and write the data using brackets :-


6 12x

HCF ?6

6( )x 2

8 12a b

HCF ?4

4( )2a 3b


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AlgebraAlgebra

Simply find the HCF for a given set of data and write the data using brackets :-


am an

HCF ?a

( )a m n

29 6x x

HCF ?3x

3 ( )x 3 2x

19 Apr 202319 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.comw

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FactorisingFactorising

Factorise the following :

(a) 3x + 6

(b) 4xy – 2x

(c) 6a + 7a2

(d) y2 - y

3(x + 2)

2x(2y – 1)

a(6 + 7a)

y(y – 1)

Be careful !

S3 Credit



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AlgebraAlgebraFactorising – The Common Factor

8-aug-15created by mr. lafferty maths dept. simplifying algebraic expressions removing brackets...

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