2-May-15Created by Mr. Lafferty Maths Dept. Algebra Removing Brackets & Simplifying Factors Simple Factorising S4

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

AlgebraAlgebraw

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Removing Brackets & Simplifying

Factors

Simple Factorising

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Starter QuestionsStarter Questionsw

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1. A TV has be reduced in the sale

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

2. 5% of 300p

3. Tidy up the expression

5y + 3d +4d + 10y

4. Find the area and perimeter of the shape.6cm

2cm

2cm

3cm

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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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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.

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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 Bracket

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-2(h + 5) =-2h - 10

Example 3

-(g - 9) = -g + 9

Example 4



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8 +2(h + 3) =8 + 6

Example 4



+ 2hNow tidy up !

+ 14= 2h

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

Example 5



+ 2Now tidy up !

+ 6= -2y

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y - (4 - y) = y + y

Example 6



- 4

= 2y - 4Now tidy up !

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a(y - 1) =ay - a

Example 7

p(w - 6) =pw- 6p

Example 8



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x(x + 3) =x2 + 3x

Example 9

3q(3q -2m) =9q2 - 6mq

Example 10




Now try Ex 1Ch15 (page 172)

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AlgebraAlgebraRemoving Brackets & SimplifyingS4

Starter QuestionsStarter Questions

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

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(a) a (6h – 3x)

Q2. True or false

Q3. Write down all the number that divide into 12 without leaving a remainder.

5 1 4 11

6 3 3 3

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18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.com

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To identify factors using To identify factors using factor pairsfactor pairs

1. To explain that a factor divides into a number without leaving a remainder

2. To explain how to find Highest Common Factors

2.2. Find HCF for two numbers Find HCF for two numbers by comparing factors.by comparing factors.

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FactorsFactorsUsing FactorsS4


FactorsFactorsw

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Factors

Example : Find the factors of 56.

F56 = 1 and 56

2 and 28

Numbers that divide into 56 without leaving a remainder

4 and 14

7 and 8

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FactorsFactors

18 Apr 202318 Apr 2023 Created by Mr. Created by Mr. [email protected]@mathsrevision.comw

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Highest Common Factor

We need to write out all factor pairs in order to find

the Highest Common Factor.

HighestCommonFactor

LargestSameNumber

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F12 = 1 and 12

2 and 6

3 and 4

F8 = 1 and 8

2 and 4

FactorsFactors


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HCF = 4

Highest Common FactorS4

F2b = 1 and 2b

2 and b

F ab = 1 and ab

a and b

FactorsFactorsw

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HCF = b

Highest Common FactorS4

2 and 5x

F4x =1, and 4x

FactorsFactors


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HCF = x

Fx2 = 1 and x2

Highest Common Factor

F5 = 1 and 5

Example : Find the HCF of 5 and 10x.

HCF = 5

F10x = 1, and 10x

5 and 2x

10 and x

2 and 2x

4 and x

x and x

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FactorsFactors

Find the HCF for these terms

(a) 16w and 24w

(b) 9y2 and 6y

(c) 4h and 12h2

(d) ab2 and a2b

8w

3y

4h

ab

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18 Apr 202318 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty

Now try Ex 2

Ch15 (page 173)

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FactorsFactorsS4

Starter QuestionsStarter Questions

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

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Q2. Write out in full

Q3. True or False all the factors of 5x2 are1, x, 5

34.85 10

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18 Apr 202318 Apr 2023 Created by Mr. [email protected] by Mr. [email protected]

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To identify the HCF for To identify the HCF for given terms.given terms.

1. To show how to factorise terms using the Highest Common Factor and one bracket term.

2.2. Factorise terms using the Factorise terms using the HCF and one bracket term.HCF and one bracket term.

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FactorisingFactorisingUsing FactorsS4


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 startedS4


FactorisingFactorisingw

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Example

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

2. HCF goes outside the bracket 2( )

3. To see what goes inside the bracketdivide each term by HCF2x2 ÷ 2 = x2

4xy ÷ 2 = 2xy 2(x2- 2xy +3)

Factorise 2x2 – 4xy + 6

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6 ÷ 2 = 3

Check by multiplying out the bracket to get back to where

you started


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FactorisingFactorising

Factorise the following :

(a) 3x + 6

(b) 4xy – 2x

(c) 6a + 7a2

(d) xy2 -xy + 4x

3(x + 2)

2x(2y – 1)

a(6 + 7a)

x(y2 – y + 4)

Be careful !

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Now try Ex 3

Ch15 (page 175)

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FactorisingFactorisingS4

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2-May-15Created by Mr. Lafferty Maths Dept. Algebra Removing Brackets & Simplifying Factors Simple Factorising S4