S4 General Brackets Factorising TJ Chapter15

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28-Apr-13 Created by Mr. Lafferty Maths Dept.

Algebra

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s r e v i s i o n . c o m

Removing Brackets & Simplifying

Factors

Simple Factorising

Starter Questions

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1. A TV has be reduced in the sale

by 20%. It 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

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s r e v i s i o n . c o m Learning Intention

Success Criteria

1. Explain how to removebrackets and simplify.

1. Understand how to removebrackets

AlgebraRemoving Brackets & Simplifying

3. Tidy up after removingbrackets.

2. Apply rules integer numbers.

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3(b + 5) = 3b + 15

Example 1

4(w - 2) = 4w - 8

Example 2

28-Apr-13 Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

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

Example 3

-(g - 9) = -g + 9

Example 4

Removing a

Single Bracket

Be carefulwith

negatives !!

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

Example 4

Removing a

Single Bracket

Be carefulonly multiply

everything inside

the bracket

+ 2hNow tidy up !

+ 14= 2h

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

Example 5

Removing a

Single Bracket

everything inside

the bracket

+ 2Now tidy up !

+ 6= -2y

y - (4 - y) = y + y

Example 6

Removing a

Single Bracket

everything inside

the bracket

Now tidy up !

a(y - 1) = ay - a

Example 7

p(w - 6) = pw - 6p

Example 8

Removing a

Single Bracket

x(x + 3) = x2 + 3x

Example 9

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

Example 10

Removing a

Single Bracket

Now try Ex 1Ch15 (page 172)

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AlgebraRemoving Brackets & SimplifyingS4

Starter Questions

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s r e v i s i o n .

Q1. Multiply out

(a) a (6h–

3x)Q2. True or false

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

5 1 4 11

6 3 3 3

Learning Intention Success Criteria

1. To identify factors usingfactor pairs

1. To explain that a factordivides into a numberwithout leaving aremainder

2. To explain how to find

Highest Common Factors

2. Find HCF for two numbersby comparing factors.

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s r e v i s i o n .

Factors

Using FactorsS4

Factors

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s r e v i s i o n .

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

Factors

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Highest Common Factor

We need to write out all factor pairs in orderto find

the Highest Common Factor.

Highest

CommonFactor

Largest

SameNumber

F12 = 1 and 12

2 and 6

3 and 4

F8 = 1 and 8

2 and 4

Factors

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s r e v i s i o n . c o m Example : Find the HCF of 8 and 12.

HCF = 4

Highest Common FactorS4

F2b = 1 and 2b2 and b

F ab = 1 and aba and b

Factors

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s r e v i s i o n . c o m Example : Find the HCF of ab and 2b.

HCF = b

Highest Common FactorS4

2 and 5x

F4x = 1, and 4x

Factors

28-Apr-13 Created by Mr. Lafferty@mathsrevision.com w w w . m a t h

s r e v i s i o n . c o m Example : Find the HCF of 4x and x2.

HCF = x

= 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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Factors

Find the HCF for these terms

(a) 16w and 24w

(b) 9y2 and 6y

(c) 4h and 12h2

(d) ab2 and a2b

28-Apr-13 Created by Mr. Lafferty

Now try Ex 2

Ch15 (page 173)

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FactorsS4

Starter Questions

Q1. Expand out a (4y – 3x) -2y

Q2. Write out in full

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

34.85 10

28-Apr-13 Created by Mr. Lafferty@www.mathsrevision.com

Learning Intention Success Criteria

1. To identify the HCF forgiven terms.

1. To show how to factoriseterms using the HighestCommon Factor and onebracket term.

2. Factorise terms using theHCF and one bracket term.

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Factorising

Using FactorsS4

Factorising

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Example Factorise 3x + 15

1. Find the HCF for 3x and 15 32. 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 multiplyingout the bracket to get

back to where youstarted

Factorising

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Example

1. Find the HCF for 2x2

, 4xy and 6 22. HCF goes outside the bracket 2( )

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

4xy ÷ 2 = 2xy 2(x2- 2xy +3)

Factorise 2x2 – 4xy + 6S4

6 ÷ 2 = 3

Check by multiplyingout the bracket to get

back to where youstarted

Factorising

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)

Becareful !

Now try Ex 3

Ch15 (page 175)

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Factorising

S4 General Brackets Factorising TJ Chapter15

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