mth 3-14a mth 4-14a mth 4-14b 9-jun-15created by mr. lafferty maths dept. simplifying algebraic...

MTH 3-14aMTH 4-14aMTH 4-14b

18 Apr 202318 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


18 Apr 202318 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. Understand and be able Understand and be able too simplify simple too simplify simple algebraic expressions by algebraic expressions by collecting ‘ like terms.’collecting ‘ 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 )


RuleMultiply the numbers

together

multiply the letters together.


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

AlgebraAlgebra

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

Removing brackets

3(b + 5) =3b + 15

Example 1

4(w - 2) =4w - 8

Example 2

Apr 18, 2023Apr 18, 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

Removing aRemoving aSingle BracketSingle BracketMTH 3-14a

MTH 4-14aMTH 4-14b

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2(y - 1) =2y - 2

Example 3

7(w - 6) =7w- 42

Example 4



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8(x + 3) =8x+ 24

Example 5

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

Example 6



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

3(x + 3) =3x + 9


Removing aRemoving aSingle BracketSingle Bracket

x+3

x+3

x+3


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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.

Removing bracketsMTH 3-14aMTH 4-14aMTH 4-14b

= 4(y + 5)

(i) A = L x B

(ii) = 4(y + 5)= 4y + 20



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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. We are learning how to remove brackets and simplify.

1. Understand how to remove brackets

AlgebraAlgebraRemoving Brackets & Simplifying

2. Understand the need to show clear working.

3. Apply to context questions.

a(b + 5) =ab + 5a

Example 1

p(w - 2) =pw - 2p

Example 2



MTH 4-14aMTH 4-14b

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y(y - 1) = y2 - y

Example 3

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

Example 4



MTH 4-14aMTH 4-14b

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

Example 5

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

Example 6



MTH 4-14aMTH 4-14b

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-(x + y) = -x - y

Example 7

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

Example 8



MTH 4-14aMTH 4-14b

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

Example 9

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

Example 10



- 3y= 19 - 3y

+ 3y

Tidy Up

= -15 + 3y


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Tidy Up

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


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Example 12 : Find area of the orange border



(x - 2)10

x

12 Area =Big Rec – Small Rec

= 12x – 10(x - 2)

= 12x

= 2x + 20


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-10x+ 20

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

Example 13

Example 14


= 3m - 14

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

Tidy Up

Removing Two Single Removing Two Single BracketsBrackets


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Tidy Up

Calculate difference if

y = 14

Diff = 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= 3y - 8



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- 4y + 20

Calculate difference if

x = 4

Diff = 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

= 2x + 20



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– 7x - 7

As= 4(x - 3)


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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.

4x-3

Removing Brackets & SimplifyingMTH 3-14aMTH 4-14aMTH 4-14b

Ab= 6x

= 4x

As= 6x - 4(x - 3)= 6x = 2x + 12

- 12

- 4x+ 12



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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. We are learning how to evaluate an expression.

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

AlgebraAlgebra

2. Use previous knowledge of Number to evaluate a 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 = -1BODMAS


2a + c

= 2x3 + (-1)

= 2x3 - 1= 6 - 1

= 5

b2 – a2

= 42 – 32

= 16 – 9

= 7

2b2

= 2x(4)2

= 2x16

= 32


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Given the following information find the values of :-

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


2a2 + 3b + 30c

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

= 18 + 12 - 30

= 0



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ww

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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. We are learning the process of factorising’.

1. Understand the term factorising.

AlgebraAlgebra

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

Factorising – The Common Factor

3. Analysis answer to validate it is correct.

18 Apr 202318 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

= 5 3( x + 5 )

Check by multiplying out the bracket to get back to where

you started


= x3x3

153

18 Apr 202318 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

2x( 2x - 3y )

Factorise 4x2 – 6xy

Check by multiplying out the bracket to get back to where

you started


= 2x4x2

2x= 3y

6xy2x


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AlgebraAlgebra

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

Factorising – The Common FactorMTH 3-14aMTH 4-14aMTH 4-14b

6x – 12

= ( )6 x - 2

8a – 12b

= ( )4 2a - 3b


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AlgebraAlgebra

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

Factorising – The Common FactorMTH 3-14aMTH 4-14aMTH 4-14b

am + an

= ( )a m+ n

9f – 6f2

= ( )3f 3 - 2f

18 Apr 202318 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



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AlgebraAlgebraFactorising – The Common Factor


mth 3-14a mth 4-14a mth 4-14b 9-jun-15created by mr. lafferty maths dept. simplifying algebraic...

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