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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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