# 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

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