<< Chapter < Page Chapter >> Page >

Kyk weer na die oefening in deel B van die vorige aktiwiteit – het jy die probleme herken?

C Gemene faktore van veelterme

Presies dieselfde metode word gebruik as ons die gemene faktore van meer as twee terme moet vind.

  • Voorbeelde:

6x 3 – 3x 2 + 6x = 3x (2x 2 – x + 2)

ab 3 c – 3a 2 b 3 c + a 3 b 2 c = ab 2 c (b – 3ab + a 2 )

3a + 24a 2 + 6a 3 = 3a ( 1 + 8a + 2a 2 )

20x – 8x 2 + 16x 3 – 12x 4 +4x 5 = 4x (5 – 2x + 4x 2 – 3x 3 + x 4 )

As jy mooi kyk, sal jy oplet dat die terme wat in die hakies oorbly, nie meer enige gemene faktore het nie. Dis wat gebeur as die uitdrukking ten volle gefaktoriseer is. Jy moet altyd die grootste moontlike gemene faktor van al die terme uithaal.

Oefening:

Faktoriseer die volgende uitdrukkings volledig deur die grootste gemene faktor uit te haal:

  1. 12abc + 24ac
  2. 15xy – 21y
  3. 3abc + 18ab 2 c 3
  4. 8x 2 y 2 – 2x
  5. 2a 2 bc 2 + 4ab 2 c – 7abc
  6. 12a(bc) 2 – 8(abc) 3 + 4(ab) 2 c 3 – 20bc + 4a

Paaraktiwiteit:

Het jy opgelet dat in elke geval die aantal terme in die hakies na faktorisering presies dieselfde is as die aantal terme in die oorspronklike uitdrukking?

Verduidelik vir jou maat hoekom jy dink dat dit altyd so sal gebeur.

D Faktore van die verskil van kwadrate

In deel D van die vorige aktiwiteit moes jy hierdie drie pare tweeterme vermenigvuldig:

(a + b) (a – b) ,

(2y + 3) (2y – 3) en

(2a 2 + 3b) (2a 2 – 3b)

  • Hier is die oplossing:

(a + b) (a – b) = a 2 – b 2

(2y + 3) (2y – 3) = 4y 2 – 9

(2a 2 + 3b) (2a 2 – 3b) = 4a 4 – 9b 2

Let op dat die antwoorde ‘n baie spesifieke patroon aanneem: vierkant minus vierkant .

Ons noem dit die verskil van kwadrate of verskil van vierkante , en dit word so gefaktoriseer:

Eerste–vierkant minus tweede–vierkant

= ( eerste vierkant size 12{ sqrt { ital "eerste" - ital "vierkant"} } {} plus tweede vierkant size 12{ sqrt { ital "tweede" - ital "vierkant"} } {} ) ( eerste vierkant size 12{ sqrt { ital "eerste" - ital "vierkant"} } {} minus tweede vierkant size 12{ sqrt { ital "tweede" - ital "vierkant"} } {} )

  • Voorbeelde:

x 2 – 25 = (x + 5) (x – 5)

4 – b 2 = (2 + b) (2 – b)

9a 2 – 1 = (3a + 1) (3a – 1)

DIT WORD VAN JOU VERWAG OM GOED VERTROUD TE WEES MET DIE ALGEMEENSTE VIERKANTE EN HUL VIERKANTSWORTELS.

Hier is ‘n klompie belangrikes – voeg self ander by die lys.

2 2 = 4 3 2 = 9 (a 2 ) 2 = a4

(a 3 ) 2 = a 6

(½) 2 = ¼ 1 2 = 1

Oefening:

Faktoriseer volledig:

1. a 2 – b 2

  1. 4y 2 – 9
  2. 4a 4 – 9b 2
  3. 1 – x 2
  4. 25 – a 6
  5. a 8 – ¼
  6. 4a 2 b 2 – 81
  7. 0,25 – x 2 y 6

9. 2a 2 – 2b 2 (versigtig!)

E Gekombineerde gemene faktore en verskille van vierkante

Soos in die laaste probleem (9), is dit noodsaaklik om eers gemene faktore uit te haal, en om daarna die uitdrukking in die hakies te faktoriseer, indien moontlik.

  • Nog ‘n voorbeeld:

Faktoriseer 12ax 2 – 3ay 2

Herken eers die gemene faktor 3a, voor jy sê dat dit nie ‘n verskil van vierkante kan wees nie.

12ax 2 – 3ay 2 = 3a (4x 2 – y 2 ) Nou herken ons 4x 2 – y 2 as verskil van twee vierkante.

12ax 2 – 3ay 2 = 3a (4x 2 – y 2 ) = 3a(2x + y)(2x – y).

Oefening:

Faktoriseer volledig :

1. ax 2 – ay 4

2. a 3 – ab 2

3. 0,5a 2 x – 4,5b 2 x

4. a 5 b 3 c – abc

F Opeenvolgende verskille van vierkante

Hou jou oë oop en probeer hierdie tweeterm volledig faktoriseer: a 4 – b 4

Nou hierdie oefening – soos gewoonlik, faktoriseer volledig.

1. x 6 – 64

2. 1 – m 8

3. 3a 4 – 24b 8

4. x – x 9

G Faktore van drieterme

Bestudeer die antwoorde op hierdie vier probleme (uit ‘n vorige aktiwiteit). Die vereenvoudigde antwoorde het partykeer twee terme, partykeer drie terme en partykeer vier. Bespreek met ‘n maat wat hier aan die gang is en besluit wat die verskille veroorsaak.

Questions & Answers

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Wiskunde graad 9' conversation and receive update notifications?

Ask