1.4 Multiplication in algebra

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

5.3: $\frac{a+\mathrm{b²}}{a-b}$

5.4: (2 a b ² c )²

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 )²

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

2.2: -3 $x$ ³ - 2 y ⁵

2.3: (2 y + 2 $x$ )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: 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

 good  average  not so good

Memorandum

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

• : $\frac{2(5)(-1{)}^2}{3(5)}$

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

• : $\frac{(5)+(-1{)}^2}{5-(-1)}$

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