1.3 Addition and subtraction in algebra

Mathematics

Grade 8

The number system

(natural and whole numbers)

Module 4

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

 good  average  not so good

Memorandum

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