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4a(2a + 1) = 8a + 4a

–5a(2a + 1) = –10a 2 – 5a

a 2 (–3a 2 – 2a) = –3a 4 – 2a 3

–7a(2a – 3) = –14a 2 + 21a

Let op : Ons het ‘n uitdrukking met faktore verander na ‘n uitdrukking met terme . Ons kan ook sê: ‘n P rodukuitdrukking is nou ‘n somuitdrukking .

Oefening:

1. 3x (2x + 4)

  1. x 2 (5x – 2)
  2. –4x (x 2 – 3x)
  3. (3a + 3a 2 ) (3a)

C Eenterm × drieterm

  • Voorbeelde:

5a(5 + 2a – a 2 ) = 25a + 10a 2 – 5a 3

– ½ (10x 5 + 2a 4 – 8a 3 ) = – 5x 5 – a 4 +4a 3

Oefening:

  1. 3x (2x 2 – x + 2)
  2. –ab 2 (–bc + 3abc – a 2 c)
  3. 12a ( ¼ + 2a + ½ a 2 )

Probeer: 4. 4x (5 – 2x + 4x 2 – 3x 3 + x 4 )

D Tweeterm × tweeterm

Elke term van die eerste tweeterm word vermenigvuldig met elke term van die tweede tweeterm.

(3x + 2) (5x + 4) = (3x)(5x) + (3x)(4) + (2)(5x) + (2)(4) = 15x 2 + 12x + 10x + 8

= 15x 2 + 22x + 8 Maak altyd seker dat jou antwoord vereenvoudig is.

  • Hierdie katgesiggie sal jou help onthou hoe om twee tweeterme te vermenigvuldig:

  • Die linkeroor sê: Vermenigvuldig die eerste term van die eerste tweeterm met die eerste term van die tweede tweeterm.
  • Die ken sê: Vermenigvuldig die eerste term van die eerste tweeterm met die tweede term van die tweede tweeterm.
  • Die bekkie sê: Vermenigvuldig die tweede term van die eerste tweeterm met die eerste term van die tweede tweeterm.
  • Die regteroor sê: Vermenigvuldig die tweede term van die eerste tweeterm met die tweede term van die tweede tweeterm.

Daar is belangrike patrone in die volgende vermenigvuldigingsoefening – let baie mooi op na hulle.

Oefening:

  1. (a + b) (c + d)
  2. (2a – 3b) (–c + 2d)
  3. (a 2 + 2a) (b 2 –3b)
  4. (a + b) (a + b)
  5. (x 2 + 2x) (x 2 + 2x)
  6. (3x – 1) (3x – 1)
  7. (a + b) (a – b)
  8. (2y + 3) (2y – 3)
  9. (2a 2 + 3b) (2a 2 – 3b)
  10. (a + 2) (a + 3)
  11. (5x 2 + 2x) (x 2 – x)

E Tweeterm × veelterm

  • Voorbeeld:

(2a + 3) (a 3 – 3a 2 + 2a – 3) = 2a 4 – 6a 3 + 4a 2 – 6a + 3a 3 – 9a 2 + 6a – 9

= 2a 4 – 3a 3 – 5a 2 – 9 (vereenvoudigde vorm)

Oefening:

  1. (x 2 – 3x) (x 2 + 5x – 3)
  2. (b + 1) (3b 2 – b + 11)
  3. (a – 4) (5 + 2a – b + 2c)
  4. (–a + 2) (a + b + c – 3d)
  • Hoe goed het jy in hierdie aktiwiteit gevaar?

Aktiwiteit 3

Om faktore van sekere algebraïese uitdrukkings te vind

[lu 1.6, 2.1, 2.7]

A Faktore

Hierdie tabel toon die faktore van sekere eenterme.

Uitdrukking Kleinste faktore
42 2 × 3 × 7
6ab 2 × 3 × a × b
21a 2 b 3 × 7 × a × a × b
(5abc 2 ) 2 5 × a × b × c × c × 5 × a × b × c × c
–8y 4 –2 × 2 × 2 × y × y × y × y
(–8y 4 ) 2 –2 × 2 × 2 × y × y × y × y × –2 × 2 × 2 × y × y × y × y

Die faktore kan in enige orde geskryf word, maar as jy by die gebruiklike orde hou, sal jou werk vergemaklik word Twee van die lyste faktore in die tabel is nie in die gebruiklike orde nie – herskryf hulle in orde.

B Gemene faktore van tweeterme

  • Beskou die tweeterm 6ab + 3ac.
  • Die faktore van 6ab is 2 × 3 × a × b en die faktore van 3ac is 3 × a × c.
  • Die faktore wat in beide 6ab en 3ac voorkom, is 3 en a – hulle is gemene faktore .
  • Ons gebruik nou hakies om die gemene faktore en die res te groepeer:

6ab = 3a × 2b en 3ac = 3a × c

  • Ons faktoriseer nou 6ab + 3ac. Dit word so uiteengesit:

6ab + 3ac = 3a (2b + c).

  • ‘n Uitdrukking met terme word verander na ‘n uitdrukking met faktore .
  • Ons kan ook sê: ‘n Somuitdrukking is nou ‘n produkuitdrukking .
  • Nog voorbeelde:
  1. 6x 2 + 12x = 3x (2x + 4)
  2. 5x 3 – 2x 2 = x 2 (5x – 2)
  3. –4x 3 + 12x 2 = –4x (x 2 – 3x)
  4. 9a 2 + 9a 3 = (3a + 3a 2 ) ( 3a )

Questions & Answers

what are free good
Maillot Reply
how do you determine price change
Matri Reply
what is economics?
Yaya Reply
what is economic
Nana Reply
Economics is the study of how Individual consumer, institution and society as a whole uses its available finite resources to satisfy infinite needs and wants
Richard
Explain the following concepts using suitable exemple. 1) National budget. 2) National debt
Rosalie
what is international trade
BOBO Reply
other things remain constant.
Esale Reply
explain scarcity
Richard Reply
scarcity occurs when there are not enough resources to satisfy human's needs and wants therefore we need to allocate our resources using the price mechanism.
Isha
scarcity is when there is inadequate resources to catch the unlimited wants which would compel individual to make choice.
Prince
scarcity simply means when there's a shortages of resources to satisfy Hunan's need and wants in a particular time, which means the demand for it at the moment is higher than the supply
Abu
scarcity simply means when there's a shortages of resources to satisfy humans need and wants in a particular time, which means the demand for it at the moment is higher than it supply.
Abu
😂😂😂
Isha
That escalated real quick😂
Isha
scarcity is sometimes considered as the basic problems of economics resources r scarce because we live in a world of humans in which wants are infinite but the land labor and capital r required to satisfy those wants are limited
Nkwenti
scarcity means unlimited resources
Rena
resources are limited but human wants can not be limited
Himanshu
joint or complementary demand
Ryt Reply
what is demand
Qudus Reply
it maybe define as the amount or quantity of goods and services which a consumer is willing to buy with the ability to pay at a given price at a particular time
Habib
yesoo thanks dear
Gyamfua
Explain 3 reasons why the manufacturer may decide to sell directly to the consumers
Rosalie
why is economics a science
Isaac Reply
Because science is all about thinking by making models whether a computational or Mathematical. Economics is a social sciences because it effects society but to understand Economics we use maths so it is a Science
Amit
hi
Mony
hello
Amit
I hope.......Economic is social science because it makes new new currency of money,it is decided the country’s depend system and the system be repeated others benefits in our ...
Anik
yeah
Habib
so what is the disadvantages of mix economic system
Habib
Economics is regarded as a social science because it uses scientific methods to build theories that can help explain the behaviour of individuals, groups and organisations.
Ali
The question is: why is Economic a "science" and not why is economics a "social science?" Alright folks?
Xavier
In my own understanding of why economics is a science it bcz it deals mainly on human resources just like biology that deals in the human body why economics is science it also deals on the management of human resources all over the world bcz without economics there will be no human resources
Ogbonnaya
what is technology
Nkwenti
my response to the earlier question is, economics is a science but not a pure science like biology, chemistry and physics. The reason is that those pure science study inanimate object while economics study human being, their experiment are predictable.
raimi
Economics is a social science subject that shows the relationship between ends and scarce means with their alternative uses
Ajenifuja
what is Equilibrium?
Fatima Reply
it means equal price and equal quality
Arthur
thank u Arthur!
Fatima
😇🙏
Fatima
Thanks
Moses
Equilibrium is a state of balance in an economy. In as far as market forces are reasonably concerned, equilibrium means the state at which the quantity of goods supplied is equal to the quantity of goods demanded.
Xavier
what is labour
Ayham
labor can be define as a both physical and mental effort of man put forward towards production
Habib
name the types of demand and explain any two
ALIMAMYISLA
Joint demand Composite demand Competitive demand
Ajenifuja
Labourcan be defined as man mental and physical exertion
Ajenifuja
equilibrium is a state of balance especially between opposing forces or influences
Nkwenti
equilibrium means the state of point in which a person is satisfied and after that point if that person consumes more than the satisfaction level will decrease.
Himanshu
Equilibrium is a state of balance in and economy. that mean equal privé and equal quality e.t.c.
Rosalie
Equilibrium is a situation in which economic forces such as supply and demand balance and in the absence of extremal lnfiuences the values of economic variables will not change.
Gyamfua
what is elasticity
Motseoa Reply
difference between demand and supply
Adeyemi Reply
Demand- It is the desire of a buyer and his ability to pay for a particular commodity at a specific price. Supply- It is quantity of a commodity which is made available by the producers to its consumers at certain price.
Ali
yes OK thank you dear
Gyamfua
Demand can be defined as the ability a buyer is willing and able to pay at a specific price and in agiven period of time Supply can be defined as the ability the producer is willing to supply with a specific price
Ajenifuja
thanks
antony
what is labor force
Habib
demand represents the consumer while supply represents the firm
Nkwenti
restriction on international trade
Ayim Reply
formula for price elasticity of demand
Lognyuu Reply
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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