Algebra II:Expanding one set of brackets

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John Hodkinson 8 years, 7 months ago

Gave some feedback: Ready to use

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Nasir Firoz Khan 8 years, 7 months ago

Gave some feedback: Needs to be tested

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Created this as a copy of Expanding one set of brackets.

Name	Status	Author	Last Modified
Distributive law: expanding one set of brackets	Ready to use	Ben Brawn	13/02/2025 22:47
Factorising: Common factor	Ready to use	Ben Brawn	25/03/2025 23:43
Distributive law: expanding one set of brackets	draft	steve kilgallon	23/08/2017 11:12
Expanding one set of brackets	Needs to be tested	Nasir Firoz Khan	05/08/2016 16:23
Distributive law: expanding one set of brackets	draft	Nasir Firoz Khan	29/07/2016 12:57
Algebra II:Expanding one set of brackets	Ready to use	Nasir Firoz Khan	12/08/2016 15:30
Algebra II:Expanding one set of brackets	Ready to use	Nasir Firoz Khan	12/08/2016 16:16
Rachel's copy of Distributive law: expanding one set of brackets	draft	Rachel Staddon	20/04/2017 14:50
Distributive law: expanding one set of brackets	draft	Owen Jepps	11/01/2018 06:07
Marlon's copy of Factorising: Common factor	draft	Marlon Arcila	03/02/2018 16:30
Algebra II:Expanding one set of brackets	draft	heike hoffmann	14/11/2018 21:00
Factorising: Common factor	Ready to use	heike hoffmann	14/11/2018 21:07
Gemeenschappelijke factor afzonderen	draft	Johan Maertens	20/08/2019 15:38
Joshua's copy of Distributive law: expanding one set of brackets	draft	Joshua Calcutt	06/08/2019 05:55
Distributive law: expanding brackets general	Ready to use	Don Shearman	02/02/2023 23:55
Distributive law: expanding one set of brackets: student types entire answer	Ready to use	Ben Brawn	13/02/2025 22:44
Distributive law: negative sign outside of brackets	Ready to use	Ben Brawn	13/02/2025 21:42

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Question statement

In the following questions, expand the bracket and express in linear variables.

For more information, please check this video- https://www.youtube.com/watch?v=9r6_wDpxKjQ

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	20
b	integer	15
c	integer	5
m	integer	300
n	integer	100

			Name	Type	Generated Value

d	integer	-3
f	integer	7
g	integer	8
p	integer	-21
q	integer	-24

			Name	Type	Generated Value

s	integer	9
t	integer	17
u	integer	5
k	integer	-1
v	integer	-9
w	integer	-17
o	integer	-5

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..20)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Gap 0." - Minimum accepted value
"Part a)" → "Gap 0." - Maximum accepted value
"Part a)" → "Gap 1." - Minimum accepted value
"Part a)" → "Gap 1." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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1. Step Information only
Part b) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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1. Step Information only
Part c) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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1. Step Information only

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

The expression $\var{a}(\var{b}x + \var{c})$ is factorised (written as a product), we can expand the expression (so it is written as a sum) to get

Gap 0. $x$ + Gap 1.

Advice

Expanding brackets involves removing the brackets from an expression by multiplying out the brackets. This is achieved by multiplying every term inside the bracket by the term outside the bracket.

Example 1- Expand $3(x+6)$

a) Remember to multiply every term inside the brackets by the term outside:

$3(x+6) = 3x + 3\times 6 = 3x + 18$

b) When multiplying out double brackets, every term in the first pair of brackets must be multiplied by each term in the second. When expanding brackets, be very careful when dealing with negative numbers. Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:

$6 (4 a - 10) = 24 a - 60$

Answers:

In part a)

We start by multiplying every term inside the bracket by the number outside.

$\var{a}(\var{b}x + \var{c})=$

$\var{a}\times\var{b} x + \var{a}\times\var{c}$

= $\var{m}x + \var{n}$

In part b), a negative times a positive gives a negative, but multiplying two negatives gives a positive:

$\var{d}(\var{f}a - \var{g})=$

$\var{d}\times\var{f} a + \var{-d}\times\var{g}$

= $\var{p}a + \var{-q}$

In part c), a negative times a positive gives a negative, but multiplying two negatives gives a positive:

$-(\var{s}x-\var{t}y+\var{u})=$

$\var{k}\times\var{s} x - (\var{k}\times\var{t})y + (\var{k}\times\var{u})$

= $\var{v}x+ \var{-w}y - \var{-o}$

$6 (4 a - 10) = 24 a - 60$

Give a worked solution to the whole question.

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This question is used in the following exam:

International Summer School: Basic algebra by Lee Fawcett in Lee's workspace.

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John Hodkinson 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

John Hodkinson 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Algebra II:Expanding one set of brackets

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

John Hodkinson 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

John Hodkinson 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`