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    By: SiyavulaAs a part of collection: "Mathematics Grade 8"

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Multiplication in algebra

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 8

THE NUMBER SYSTEM

(Natural and whole numbers)

Module 5

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 23 x 3² x 33 = .........................

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

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

1.4: a² x a² x a3 = .........................

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: 30 = .........................

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

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

1.8: 31 = .........................

1.9: 1200 = .........................

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

2.1: a² =

2.2: 2ab =

2.3: -3(a + b) =

2.4: 4(a)² =

2.5: (a3)² =

2.6: (3a²)3 =

2.7: 2p x 3p =

2.8: ab² x a²b3 x ab6 =

2.9: ( 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}a3)4 =

2.10: 2(a3)² =

2.11: 6(2a - 3b) =

2.12: -7a(a² - 2b² ) =

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 + a4

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

3.1.3: 3a x 2a²b + 5a² x (-3ab)

3.1.4: -5a(a - b3) + 7ab3 - 2a5

3.1.5: -3(a²b4)² - 5a3(-2a4b²)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: 5a² - 3b

5.2: 2ab23a2ab23a size 12{ { {2 bold "ab" rSup { size 8{2} } } over {3a} } } {}

5.3: a+b²a−ba+b²a−b size 12{ { {a" "+" "b²} over {a` - `b} } } {}

5.4: (2ab²c)²

5.5: -3ab3 - 2ab3c

HOMEWORK ASSIGNMENT 1

1. Simplify each of the following:

1. (a5)6

1.2: 5(3a - 7a)²

1.3: -5(3a - 2b)

1.4: (3a)² . [ (2a)² ]3

1.5: p x 2 x m x q

1.6: w² x 3b x 1/3 b x w

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

1.8: (3a)² (2a) + (4a²) (-2a)

1.9: (5ab²)4 - (- 6b6a4)

1.10: -6a²b ( 2a² - 3ab3 + 5)

2. Supposing that xx size 12{x} {} = -2 and y = -1 , determine the value of ...

2.1: (2y)(2 xx size 12{x} {})²

2.2: -3 xx size 12{x} {}3 - 2y5

2.3: (2y + 2 xx size 12{x} {})²

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: 4m - 2n - 3q

3.3: 2(m² + q²) - n²

3.4: m/3 + n/4 - q

3.5: 3m(n + q) - 2(m + n²)

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 5a4 kilometres per hour.What is the distance that the bus can complete in (5a3 + 5a - 6) hours?

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

What will these purchases cost in total?

Assessment

Table 1
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

Table 2
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.     >          
Table 3
Comments by parents:   Comments by teacher:
     
     
     
Signature: Date:   Signature: Date:

Memorandum

CLASWORK ASSIGNMENT 1

  • :23
  • :212
  • :a 3
  • :a 7

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

  • :2a – 2b
  • :1

1.7 :a

  • :3
  • :1
  • :a x a
  • :2 x a x b
  • :–3a – 3b
  • :4 x a x a = 4a2
  • :a3 x a3 – a6
  • :27a6
  • :6p2
  • :a 4 b 11
  • : 116116 size 12{ { {1} over {"16"} } } {}a12
  • :2a6
  • :12a – 18b
  • :–7a3 + 14ab2

3.1 :1: ( )

:2: of

3: x or ÷ from left to right

4: + or – from left to right

  • :a5 + a4
  • :2a + 2b – 3a + 3b = -a + 5b
  • :–18a6b2
  • : –5a2 + 5ab3 + 7ab3 – 2a5

:=-5a2 + 12ab3 + 7ab3 – 2a5

  • :–3a4b8 + 10a15b6

4. put another value in unknown place

  • :5(5)2–3(–1)

= 125 + 3 = 128

  • : 2(5)(−1)23(5)2(5)(−1)23(5) size 12{ { {2 \( 5 \) \( - 1 \) rSup { size 8{2} } } over {3 \( 5 \) } } } {}

= 10151015 size 12{ { {"10"} over {"15"} } } {} = 2323 size 12{ { {2} over {3} } } {}

  • : (5)+(−1)25−(−1)(5)+(−1)25−(−1) size 12{ { { \( 5 \) + \( - 1 \) rSup { size 8{2} } } over {5 - \( - 1 \) } } } {}

= 6666 size 12{ { {6} over {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

  • :930
  • :5(–4a)2 = 80a2
  • :–15a + 10b
  • :9a2.64a6 = 576a8
  • :2mpq
  • :b 2 w 3
  • :–15a2 + 25a2b
  • :6a3 – 8a3 = –2a3
  • :625a4b8 + 6a4b6
  • :–12a4b + 18a3b4 – 30a2b
  • :[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 : 2323 size 12{ { {2} over {3} } } {} + −34−34 size 12{ { { - 3} over {4} } } {} – 5

= −14−14 size 12{ { { - 1} over {4} } } {} – 5 = 5 1414 size 12{ { {1} over {4} } } {}

3.5 :3(2)[–3 + 5] – 2 [2 + (–3)2]

= 6[2] – 2[11]

= 12 – 2

= –10

  • :5a4(5a3 + 5a – 6)

= 25a7 + 25a5 – 30a4

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

= 4a2b – 4ab2 + 8abc + 10a2b + 25ab2 – 15abc

= 14a2b + 21ab2 – 7abc

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