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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 )

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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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