# 1.3 Addition and subtraction in algebra

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## Addition and subtraction in algebra

CLASS ASSIGNMENT 1

• Discover more and more about addition and subtraction in ALGEBRA ….
• When we do addition and subtraction in Algebra, we can only add together or subtract like terms (terms of the same type) from one another.
• e.g. 3 a + 5 a = 8 a ( a is the same for both terms)
• e.g. 3 a + 5 a ² (cannot be added together, because one term is a and the other a ² - not of the same type)
• remember: -8(+5) means: -8 x (+5) = -40(two signs must not be placed next to one another; multiply the two signs by one another)

1. Can you still do the following with integers?

1.1: -8 - 12 + 8

1.2: 7 - (+8) - (-6)

1.3: 15 - (-9) + (+7)

1.4: 2(-6) - 5(-6)

1.5: 50 - 70 + 15

2. WOW! Look at this! Quite easy….

2.1 2 a + 2 a = (yes, they are alike; I can add)

2.2 3 a - 6 y + 7 a + 15 y = (look for like terms)

3 a + 7 a =

-6 y + 15 y =

(now write the answer alongside the question)

2.3 Add the following expressions together:

2.3.1: 6 a - 7 b - 9 c ; -7 a + 15 b - 29 c

2.3.2: -9 a ² - 16 a + 17 b ; -17 a ² -40 ; -29 b + 30

3. How about subtracting? Look at the following example:Subtract 6 from 15 . How would you write this? 15 - (+6) = 15 - 6 = 9

Explanation: (-) x (+) = (-) THEREFORE: 15 - 6

Look at the following: Subtract -6 a + 5 b from 16 a - 3 b

It will look like this: 16 a - 3 b - (-6 a + 5 b )

= 16 a - 3 b + 6 a - 5 b (multiply (-) within the brackets)

= 16 a + 6 a - 3 b - 5 b

= 22 a - 8 b

• Important: Begin by deciding which expression should be written first!

3.1 Calculate each of the following:

3.1.1 Subtract the second from the first: -7 a + 3 ; 6 a - 9

3.1.2 Subtract -7 a ² - 5 a + 8 from 18 a ² - 15

3.1.3 Reduce -15 $x$ ² - 7 $x$ + 20 by -6 $x$ ² + 76

HOMEWORK ASSIGNMENT 1

1. Add the following expressions together: -3 p ² - 2 p - 5 ; 6 p ² + 8 ; -15 p - 28

2. Subtract -5 p ² - 3 p from 8 - 7 a ²

3. Subtract 6 a - 8 y from 1

4. 3 a 3 + 6 a - 7 a - 5 - 2(8 a 3 - 4 a ² + 17 a + 8) - 15 a

5. Increase 6 p + 15 y - 3 a b y -13 y - 18 p + 34 a

6. By how much is -8 a ² + 6 a bigger than 15 a ² + 3 a - 5 ?

7. By how much is 4 a ² - 5 a + 1 smaller than 16 a ² + 3 a - 7 ?

8. What must be added to 5 a ² + 3 a to get -3 a + 6 ?

Assessment

 Assessment of myself: by myself: Assessment by Teacher: I can…    1 2 3 4 Critical Outcomes 1 2 3 4 Identify like terms in an expression; (Lu 2.8.1; 2.8.2) Critical and creative thinking Add like terms together; (Lu 2.8.2; 2.8.4) Collaborating Subtract like terms from each other; (Lu 2.8.2; 2.8.4) Organising en managing Add and subtract constant values; (Lu 2.8.4) Processing of information Add a range of expressions together; (Lu 2.8.2; 2.8.4; 2.8.6) Communication Subtract a range of expressions from each other. (Lu 2.8.2; 2.8.4; 2.8.6) Problem solving 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: Parent signature: Date Signature: Date :

## Class assignment 1

• -12
• 5
• 31
• 18
• –5
• 4a
• 10 a + 9 a
• - a + 8 b – 38 c
• –26 a 2 – 16 a – 12 b – 10
• -7 a + 3 – (6 a – 9)

= -7 a +3 – 6 a + 9

= -13 a + 12

• 18 a 2 – 15 – (-7 a 2 – 5 a + 8)

= 18 a 2 – 15 + -7 a 2 + 5 a – 8

= 25 a 2 + 5 a – 23

• -15 x 2 – 7 x + 20 – (-6 x 2 + 76)

= -15 x 2 – 7 x + 20 + -6 x 2 – 76

= -9 x 2 – 7 x – 56

## Homework assignment 1

1. 3 p 2 – 17 p – 25

2. 8 – 7 a 2 – (-5 p 2 – 3 p )

= 8 – 7 a 2 + 5 p 2 + 3 p )

-2 a 2 + 3 p + 8

3. 1 – (6 a – 8 y ) = 1 – 6 a + 8 y

4. 3 a 3 + 6 a – 7 a – 5 – 16 a 3 + 8 a 2 – 34 a – 16 – 15 a

= -13 a 3 + 8 a 2 – 50 a – 21

5. 24 p + 28 y – 37 a

6. -23 a 2 + 3 a + 5

7. 12 a 2 + 8 a – 8

8. -6 a + 6 – 5 a 2

#### Questions & Answers

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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da
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Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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Alexandre
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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?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
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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
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Anam
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Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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