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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

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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