# 1.4 Multiplication in algebra

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## Multiplication in algebra

CLASS ASSIGNMENT 1

• Discover more and more about multiplication in ALGEBRA!

1. Indicate what the following will be equal to...

1.1: 2 x 2 x 2 = ....................... (and what the exponent form will be .....................)

1.2: 2² x 2² x 2 3 x 3² x 3 3 = .........................

(and what the exponent form will be ......................... )

• :a x a x a = .........................

1.4: a ² x a ² x a 3 = .........................

Now write out a general rule for the multiplication of exponents:

1.5: 2( a - b ) = .........................

distributive law: (2 x a ) - (2 x b )

1.6: 3 0 = .........................

1.7: a ( a + b ) 0 = .........................

Therefore: (anything) to the power of 0 = .........................

1.8: 3 1 = .........................

1.9: 1 200 = .........................

2. What does each of the following mean? Also provide the simplified answer for each one

2.1: a ² =

2.2: 2 a b =

2.3: -3( a + b ) =

2.4: 4( a )² =

2.5: ( a 3 )² =

2.6: (3 a ²) 3 =

2.7: 2 p x 3 p =

2.8: a b² x a ² b 3 x a b 6 =

2.9: ( $\frac{1}{2}$ a 3 ) 4 =

2.10: 2( a 3 )² =

2.11: 6(2 a - 3 b ) =

2.12: -7 a ( a ² - 2 b ² ) =

3. Can you recall the order of operations for the following? Write it down.

3.1 Now make use of everything you have learnt up till now to calculate the following:

3.1.1: a x a x aaa + a 4

3.1.2: 2( a + b ) - 3( a - b )

3.1.3: 3 a x 2 a ² b + 5 a ² x (-3 a b )

3.1.4: -5 a ( a - b 3 ) + 7 a b 3 - 2 a 5

3.1.5: -3( a ² b 4 )² - 5 a 3 (-2 a 4 b ²) 3

4. What is the meaning of the word substitution?

Provide an example as explanation:

5. Supposing that a = 5 ; b = -1 and c = 3 , calculate the value of each of the following:

5.1: 5 a ² - 3 b

5.2: $\frac{2{\text{ab}}^{2}}{3a}$

5.3: $\frac{a\text{}+\text{}\mathrm{b²}}{a-b}$

5.4: (2 a b ² c

5.5: -3 a b 3 - 2 a b 3 c

HOMEWORK ASSIGNMENT 1

1. Simplify each of the following:

1. ( a 5 ) 6

1.2: 5(3 a - 7 a

1.3: -5(3 a - 2 b )

1.4: (3 a )² . [ (2 a )² ] 3

1.5: p x 2 x m x q

1.6: w ² x 3 b x 1 / 3 b x w

1.7: -5 a ( 3 a - 5 a b)

1.8: (3 a )² (2 a ) + (4 a ²) (-2 a )

1.9: (5 a b ²) 4 - (- 6 b 6 a 4 )

1.10: -6 a ² b ( 2 a ² - 3 a b 3 + 5)

2. Supposing that $x$ = -2 and y = -1 , determine the value of ...

2.1: (2 y )(2 $x$

2.2: -3 $x$ 3 - 2 y 5

2.3: (2 y + 2 $x$

3. Supposing m = 2 ; n = -3 en q = 5, determine the value of each of the following expressions:

3.1: m + n + q

3.2: 4 m - 2 n - 3 q

3.3: 2( m ² + q ²) - n ²

3.4: m / 3 + n / 4 - q

3.5: 3m( n + q ) - 2( m + n ²)

4. A challenge: See if the knowledge that you have acquired is able to help you solve the problems that follow.

4.1 The average speed of an Intercape Mainliner is 5 a 4 kilometres per hour.What is the distance that the bus can complete in (5 a 3 + 5 a - 6) hours?

4.2 Miss South Africa buys ( a - b + 2 c ) litres of milk at 4 ab rands per litre and 5 ab litres of fruit juice at (2 a + 5 b - 3 c ) rands per litre.

What will these purchases cost in total?

Assessment

 Assessment of myself: by myself: Assessment by Teacher: I can…    1 2 3 4 Critical Outcomes 1 2 3 4 write expressions in exponent form; (Lo 2.2; 1.6.3) Critical and creative thinking successfully add exponents together; (Lo 2.2; 1.6.3) Collaborating successfully subtract exponents from each other; (Lo 2.2; 1.6.3) Organising en managing successfully multiply exponents with each other; (Lo 2.2; 2.8.3&.4) Processing of information solve expressions with brackets; (Lo 2.2; 2.8.5) Communication apply the correct order of calculations; (Lo 2.2; 2.8.5) Problem solving determine values of expressions with substitution. (Lo 2.2; 2.8.5; 1.6.2; 1.6.3)
 Independence

good average not so good

 Comments by the learner: My plan of action: My marks: I am very satisfied with the standard of my work. < Date : I am satisfied with the steady progress I have made. Out of: I have worked hard, but my achievement is not satisfactory. Learner : I did not give my best. >
 Comments by parents: Comments by teacher: Signature: Date : Signature: Date :

## Claswork assignment 1

• :2 3
• :2 12
• :a 3
• :a 7

Multiply and bases are the same: you add the exponents.

• :2 a – 2 b
• :1

1.7 :a

• :3
• :1
• :a x a
• :2 x a x b
• :–3 a – 3 b
• :4 x a x a = 4 a 2
• :a 3 x a 3 a 6
• :27 a 6
• :6 p 2
• :a 4 b 11
• : $\frac{1}{\text{16}}$ a 12
• :2 a 6
• :12 a – 18 b
• :–7 a 3 + 14 ab 2

3.1 :1: ( )

:2: of

3: x or ÷ from left to right

4: + or – from left to right

• :a 5 + a 4
• :2 a + 2 b – 3 a + 3 b = - a + 5 b
• :–18 a 6 b 2
• : –5 a 2 + 5 ab 3 + 7 ab 3 – 2 a 5

:=-5 a 2 + 12 ab 3 + 7 ab 3 – 2 a 5

• :–3 a 4 b 8 + 10 a 15 b 6

4. put another value in unknown place

• :5(5) 2 –3(–1)

= 125 + 3 = 128

• : $\frac{2\left(5\right)\left(-1{\right)}^{2}}{3\left(5\right)}$

= $\frac{\text{10}}{\text{15}}$ = $\frac{2}{3}$

• : $\frac{\left(5\right)+\left(-1{\right)}^{2}}{5-\left(-1\right)}$

= $\frac{6}{6}$ = 1

• :[2(5)(–1) 2 (3)] 2

= [30] 2 = 900

• :–3(5)(–1) 3 –2(5)(–1) 3 (3)

= 15 + 30 = 45

## Classwork assignment1

• :9 30
• :5(–4 a ) 2 = 80 a 2
• :–15 a + 10 b
• :9 a 2 . 64 a 6 = 576 a 8
• :2 mpq
• :b 2 w 3
• :–15 a 2 + 25 a 2 b
• :6 a 3 – 8 a 3 = –2 a 3
• :625 a 4 b 8 + 6 a 4 b 6
• :–12 a 4 b + 18 a 3 b 4 – 30 a 2 b
• :[2(–1)][2(2)] 2

=(–2)(16) = –32

• :–3(–2) 3 –2(–1) 5

= 24 + 2 = 26

• :[2(–1) + 2(–2)] 2

= [–2–4]

= (–6) 2

= 36

• :2 + (–3) + = 4
• :4(2) – 2(–3) – 3(5)

= 8 + 6 – 15 = –1

• :2[(2) 2 + (5) 2 ] – (–3) 2

= 2[4 + 25] – (–3) 2

= 58 – 9 = 49

3.4 : $\frac{2}{3}$ + $\frac{-3}{4}$ – 5

= $\frac{-1}{4}$ – 5 = 5 $\frac{1}{4}$

3.5 :3(2)[–3 + 5] – 2 [2 + (–3) 2 ]

= 6[2] – 2[11]

= 12 – 2

= –10

• :5 a 4 (5 a 3 + 5 a – 6)

= 25 a 7 + 25 a 5 – 30 a 4

• :4 ab ( a b + 2 c ) + 5 ab (2 a + 5 b – 3 c )

= 4 a 2 b – 4 ab 2 + 8 ab c + 10 a 2 b + 25 ab 2 – 15 ab c

= 14 a 2 b + 21 ab 2 – 7 ab c

#### Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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
hey
Giriraj
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, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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