<< Chapter < Page Chapter >> Page >

Inleiding

In hierdie hoofstuk sal jy leer hoe om met algebraïese uitdrukkings te werk. Hersiening van vorige faktorisering en vermenigvuldiging van uitdrukkings sal dus nodig wees voordat die nuwe leerstof uitgebrei word vir Graad 10.

Hersiening van vorige werk

Die volgende behoort bekend te wees, maar ons gee 'n paar voorbeelde ter herinnering.

Dele van uitdrukkings

Wiskundige uitdrukkings is soos sinne en elke deel het 'n spesifieke naam. Jy behoort vertroud te wees met die volgende name wat die dele van wiskundige uitdrukkings beskryf.

a · x k + b · x + c m = 0 d · y p + e · y + f 0
Naam Voorbeelde (geskei deur kommas)
term a · x k , b · x , c m , d · y p , e · y , f
uitdrukking a · x k + b · x + c m , d · y p + e · y + f
koëffisiënte a , b , d , e
eksponent (of indeks) k , p
grondtal x , y , c
konstante a , b , c , d , e , f
veranderlike x , y
vergelyking a · x k + b · x + c m = 0
ongelykheid d · y p + e · y + f 0
binomiaal uitdrukking met twee terme
trinomiaal uitdrukking met drie terme

Produk van twee binomiale

'n Binomiaal is 'n wiskundige uitdrukking met twee terme, soos ( a x + b ) en ( c x + d ) . As hierdie twee binomiale vermenigvuldig word, is die volgende die resultaat:

( a · x + b ) ( c · x + d ) = ( a x ) ( c · x + d ) + b ( c · x + d ) = ( a x ) ( c x ) + ( a x ) d + b ( c x ) + b · d = a x 2 + x ( a d + b c ) + b d

Vind die produk van ( 3 x - 2 ) ( 5 x + 8 ) .

  1. ( 3 x - 2 ) ( 5 x + 8 ) = ( 3 x ) ( 5 x ) + ( 3 x ) ( 8 ) + ( - 2 ) ( 5 x ) + ( - 2 ) ( 8 ) = 15 x 2 + 24 x - 10 x - 16 = 15 x 2 + 14 x - 16
    .

Die produk van twee identiese binomiale, is bekend as die kwadraat (of vierkant) van binomiale en word geskryf as:

( a x + b ) 2 = a 2 x 2 + 2 a b x + b 2

Gestel die twee terme is a x + b en a x - b , dan is hulle produk:

( a x + b ) ( a x - b ) = a 2 x 2 - b 2

Dit staan bekend as die verskil van twee kwadrate (of vierkante) .

Faktorisering

Faktorisering is die omgekeerde proses van die uitbreiding van hakies. Byvoorbeeld, as hakies uitgebrei word, word 2 ( x + 1 ) geskryf as 2 x + 2 . Faktorisering sal dus begin met 2 x + 2 en eindig met 2 ( x + 1 ) . In vorige grade het ons gefaktoriseer deur die uithaal van gemeenskaplike faktore en die verskil tussen twee vierkante.

Gemeenskaplike faktore

Faktorisering deur die uithaal van gemeenskaplike faktore, is gebaseer daarop dat daar faktore is wat in al die terme voorkom. Byvoorbeeld, 2 x - 6 x 2 kan as volg gefaktoriseer word:

2 x - 6 x 2 = 2 x ( 1 - 3 x )

Ondersoek: gemeenskaplike faktore

Vind die grootste gemene faktore van die volgende pare terme:

(a) 6 y ; 18 x (b) 12 m n ; 8 n (c) 3 s t ; 4 s u (d) 18 k l ; 9 k p (e) a b c ; a c
(f) 2 x y ; 4 x y z (g) 3 u v ; 6 u (h) 9 x y ; 15 x z (i) 24 x y z ; 16 y z (j) 3 m ; 45 n

Verskil van twee kwadrate

Ons het gesien dat:

( a x + b ) ( a x - b ) = a 2 x 2 - b 2

In [link] dui die = teken aan dat die twee kante altyd gelyk sal wees. Dit beteken dat 'n uitdrukking in die vorm:

a 2 x 2 - b 2

gefaktoriseer kan word as:

( a x + b ) ( a x - b )

Dus,

a 2 x 2 - b 2 = ( a x + b ) ( a x - b )

Byvoorbeeld, x 2 - 16 kan geskryf word as ( x 2 - 4 2 ) wat die verskil is tussen twee kwadrate. Dus, die faktore van x 2 - 16 is ( x - 4 ) en ( x + 4 ) .

Faktoriseer volledig: b 2 y 5 - 3 a b y 3

  1. b 2 y 5 - 3 a b y 3 = b y 3 ( b y 2 - 3 a )

Faktoriseer volledig: 3 a ( a - 4 ) - 7 ( a - 4 )


  1. ( a - 4 ) is die gemene faktor
    3 a ( a - 4 ) - 7 ( a - 4 ) = ( a - 4 ) ( 3 a - 7 )

Faktoriseer 5 ( a - 2 ) - b ( 2 - a )

  1. 5 ( a - 2 ) - b ( 2 - a ) = 5 ( a - 2 ) - [ - b ( a - 2 ) ] = 5 ( a - 2 ) + b ( a - 2 ) = ( a - 2 ) ( 5 + b )

Hersien

  1. Vind die produkte / Verwyder die hakies:
    (a) 2 y ( y + 4 ) (b) ( y + 5 ) ( y + 2 ) (c) ( y + 2 ) ( 2 y + 1 )
    (d) ( y + 8 ) ( y + 4 ) (e) ( 2 y + 9 ) ( 3 y + 1 ) (f) ( 3 y - 2 ) ( y + 6 )


  2. Faktoriseer:
    1. 2 l + 2 w
    2. 12 x + 32 y
    3. 6 x 2 + 2 x + 10 x 3
    4. 2 x y 2 + x y 2 z + 3 x y
    5. - 2 a b 2 - 4 a 2 b


  3. Faktoriseer volledig:
    (a) 7 a + 4 (b) 20 a - 10 (c) 18 a b - 3 b c
    (d) 12 k j + 18 k q (e) 16 k 2 - 4 k (f) 3 a 2 + 6 a - 18
    (g) - 6 a - 24 (h) - 2 a b - 8 a (i) 24 k j - 16 k 2 j
    (j) - a 2 b - b 2 a (k) 12 k 2 j + 24 k 2 j 2 (l) 72 b 2 q - 18 b 3 q 2
    (m) 4 ( y - 3 ) + k ( 3 - y ) (n) a ( a - 1 ) - 5 ( a - 1 ) (o) b m ( b + 4 ) - 6 m ( b + 4 )
    (p) a 2 ( a + 7 ) + a ( a + 7 ) (q) 3 b ( b - 4 ) - 7 ( 4 - b ) (r) a 2 b 2 c 2 - 1


Questions & Answers

what is price surveillance?
Berry Reply
what is demand
Oluchi Reply
what are two classical macroeconomics and what're their theories say about their equations?
AMARA Reply
what is the formula for calculating elasticity
aza Reply
mpp÷APP
Umar
what is elasticity of demand?
Rita Reply
hello
Osanday
hi
SHERO
Causes of economic growth
pierre Reply
What is elasticity of demand
pierre
What are the causes of economic growth
pierre
economic growth, establishment of industry, encourage of investor's, farm productivities, creation of institutions, construction of good road etc
Oyewale
elasticity of demand can be said to be the responsiveness of demand to a change in prices
fateemah
impact of collusion in the economy referring to inefficiencies illustrated by means of graph
nondumiso Reply
The Factor price will determine the choice of techniques to produce.Expantiate
dajan
what is elasticity of demand?
Etta Reply
state and explain two types of demand
Etta
Institution involved in money market
Gande Reply
what is Economics
Kwame Reply
Economic is the study of scarcity
Kolade
Economics is the study of a lot of things. It is split up into two areas of study, Microeconomics and Macroeconomics. Microeconomics is the study of an individual's choices in the economy and Macroeconomics is the study of the economy as a whole.
The
Economics is a science that studies human scarcity
Agnes
What is Equilibrium price?
Agnes
Equilibrium is the market clearing price. The point at which quantity demanded equals quantity supplied. The point at which the supply and demand curves intersect.
The
Equilibrium price*
The
Refers to the study of how producers use limited resources to satisfy human unlimited wants
Gatoya
why is economics important
Derrick Reply
What will you do as a consumer if you are not at equilibrium?
chukwu Reply
am new I will like to know about the graph relationship
Gloria Reply
comment on WTO principle on trading system. trade without discrimination
Omben Reply
optimize z=f(x,y)=6x²-9x-3xy-7y+5y²
Alex Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Difference between extinct and extici spicies
Amanpreet Reply
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah Reply
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, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: wiskunde (graad 10) [caps]' conversation and receive update notifications?

Ask