Maria's copy of Expansion of brackets

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Maria Aneiros 5 years, 9 months ago

Created this as a copy of Expansion of brackets.

Name	Status	Author	Last Modified
Expansion of brackets	Ready to use	Bradley Bush	23/03/2020 14:02
haken met distributieve eig uitwerken	draft	Johan Maertens	08/07/2020 16:05
spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
Ida's copy of spørsmål 1	draft	Ida Landgärds	02/12/2020 15:42
Maria's copy of Expansion of brackets	draft	Maria Aneiros	29/05/2019 05:59
ahmad's copy of Expansion of brackets	draft	ahmad yahya	30/05/2019 11:27
Øystein's copy of Expansion of brackets	draft	Øystein Hildre	02/12/2020 15:42
AB5 Expand single brackets	Ready to use	Megan Oliver	09/04/2024 15:05

There are 42 other versions that do you not have access to.

Question statement

Expand the expressions below by multiplying each of the terms inside the brackets by the term outside. Give each answer in its simplest form.

Give any introductory information the student needs.

			Name	Type	Generated Value

list

List of 50 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(-10..10 except [-1,0,1] ),50)

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: `list`

[ 5, -4, 2, -10, -10, -5, 7, 2, -2, -9, 8, -8, 4, -5, -4, -3, 3, -10, -2, -4, -8, 3, 3, -10, 6, -2, -6, 6, 2, -4, 3, -7, -7, 7, 6, 9, -3, -5, 9, 5, 2, 7, 7, -8, 5, 9, 3, -10, -4, 4 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
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Part b) Gap-fill
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Part c) Gap-fill
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Part d) Gap-fill
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Part h) Gap-fill
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Part i) Gap-fill
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Part j) Gap-fill
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Gap-fill

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

$\simplify{{a[1]}({a[2]}x+{a[3]})}=$ Unnamed gap

Advice

Expand brackets using the general formula $\displaystyle a(x+c)=ax+ac$ . This means we multiply each term inside the brackets by the term outside the brackets.

It is easy to forget that the sign outside the brackets also needs to be involved in the multiplication so remember that when two of the same sign are multiplied, the resultant term is positive and when opposite signs are multiplied, the result is negative.

a)

$\begin{align} \simplify[terms]{{a[1]}({a[2]}x+{a[3]})}&= \simplify[!collectNumbers]{({a[1]}{a[2]})x+({a[1]}{a[3]})}\\& =\simplify{{a[1]}*{a[2]}x+{a[1]}{a[3]}}\text{.} \end{align}$

b)

$\begin{align} \simplify[terms]{{a[4]}({a[5]}x+{a[6]})}&= \simplify[!collectNumbers]{{a[4]}{a[5]}x+{a[4]}{a[6]}}\\&= \simplify{{a[4]}*{a[5]}x+{a[4]}{a[6]}}\text{.} \end{align}$

c)

$\begin{align} \simplify[terms]{{a[7]}({a[8]}x^2+{a[9]}y)}&= \simplify[!collectNumbers]{{a[7]}{a[8]}x^2+{a[7]}{a[9]}y}\\&= \simplify{{a[7]}*{a[8]}x^2+{a[7]}*{a[9]}y}\text{.} \end{align}$

d)

$\begin{align} \simplify[terms]{{a[10]}({a[11]}x^2+{a[12]}y)}&= \simplify[!collectNumbers]{{a[10]}{a[11]}x^2+{a[10]}{a[12]}y}\\&= \simplify{{a[10]}*{a[11]}x^2+{a[10]}*{a[12]}y}\text{.} \end{align}$

e)

$\begin{align} \simplify[terms]{{a[13]}x({a[14]}x^2+{a[15]}x+{a[16]})}&= \simplify[!collectNumbers]{{a[13]}x{a[14]}x^2+{a[13]}x{a[15]}x+{a[13]}x{a[16]}}\\&= \simplify{{a[13]}{a[14]}x^3+{a[13]}{a[15]}x^2+{a[13]}{a[16]}x}\text{.} \end{align}$

f)

$\begin{align} \simplify[terms]{{a[17]}x({a[18]}x^2+{a[19]}x+{a[20]})}&= \simplify[!collectNumbers]{{a[17]}x{a[18]}x^2+{a[17]}x{a[19]}x+{a[17]}x{a[20]}}\\&= \simplify{{a[17]}{a[18]}x^3+{a[17]}{a[19]}x^2+{a[17]}{a[20]}x}\text{.} \end{align}$

g)

$\begin{align} \simplify[terms]{{a[21]}x({a[22]}x^2+{a[23]}x)+{a[24]}x^2+{a[25]}x^3}&= \simplify[!collectNumbers]{x^2({a[21]}{a[23]})+x^2{a[24]}+x^3({a[21]}{a[22]})+x^3{a[25]}}\\&= \simplify[!collectNumbers]{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\\&= \simplify{x^2({a[21]}{a[23]}+{a[24]})+x^3({a[21]}{a[22]}+{a[25]})}\text{.} \end{align}$

h)

$\begin{align} \simplify[terms]{({a[26]}x^2+{a[27]}x^3)+{a[28]}x({a[29]}x^2+{a[30]}x)}&= \simplify[!collectNumbers]{x^2({a[26]})+x^2({a[28]}{a[30]})+x^3({a[28]}{a[29]})+x^3({a[27]})}\\&= \simplify[!collectNumbers]{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\\&= \simplify{x^2({a[26]}+{a[28]}{a[30]})+x^3({a[28]}{a[29]}+{a[27]})}\text{.} \end{align}$

i)

$\begin{align} \simplify[terms]{{a[31]}({a[32]}x+{a[33]}y)+{a[34]}x({a[42]}+{a[35]}y)}&= \simplify[!collectNumbers]{({a[31]}{a[32]})x+({a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\&= \simplify[!collectNumbers]{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\\&= \simplify{({a[31]}{a[32]}+{a[34]}{a[42]})x+{a[31]}{a[33]}y+{a[34]}{a[35]}x*y}\text{.} \end{align}$

j)

$\begin{align} \simplify[terms]{{a[36]}a^2({a[37]}+{a[38]}b)+{a[39]}b^2({a[40]}a+{a[41]}b)}&= \simplify[!collectNumbers]{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\\&= \simplify{{a[37]}{a[36]}a^2+{a[38]}{a[36]}a^2b+{a[40]}{a[39]}a*b^2+{a[39]}{a[41]}b^3}\text{.} \end{align}$

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Maria Aneiros 5 years, 9 months ago

Error in variable testing condition

Error

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Generated value: `list`

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

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Maria's copy of Expansion of brackets

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Maria Aneiros 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

Generated value: `list`