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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

so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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