Transum Software

Brackets

Expand algebraic expressions containing brackets and simplify the resulting expressions.
  Menu   Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10   Help  

This is level 10: expanding products of three binomials (cubic expressions). You will be awarded a trophy if you get at least 9 answers correct and you do this activity online.

Simplify the following expressions by removing the brackets. Order the terms in your answers so that variable terms come before the constants and the variables are in decreasing power order. Use ^2 or ^3 to insert exponents into your answer .

1

\((x+1)(x+2)(x+3)\)

☐ ✓ ✗

2

\((x+5)(x+1)(x+4)\)

☐ ✓ ✗

3

\((x+3)(x+2)(x-1)\)

☐ ✓ ✗

4

\((x-4)(x+2)(x-3)\)

☐ ✓ ✗

5

\((x-4)^2(x-3)\)

☐ ✓ ✗

6

\((x-5)^3\)

☐ ✓ ✗

7

\((2x+5)(x+2)(x-5)\)

☐ ✓ ✗

8

\((x+4)(3x+1)(x-7)\)

☐ ✓ ✗

9

\((2x+3)(x+2)(3x-1)\)

☐ ✓ ✗

10

\((2x+1)(5x+1)(x-6)\)

☐ ✓ ✗

11

\((2x-5)(3x+2)(4x-3)\)

☐ ✓ ✗

12

\((5-3x)(2x+1)(9-5x)\)

☐ ✓ ✗

Check

This is Brackets level 10. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 18 September 'Starter of the Day' page by Mrs. Peacock, Downe House School and Kennet School:

"My year 8's absolutely loved the "Separated Twins" starter. I set it as an optional piece of work for my year 11's over a weekend and one girl came up with 3 independant solutions."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity

Lemon Law

Lemon Law

A fascinating digit changing challenge. Change the numbers on the apples so that the number on the lemon is the given total. Can you figure out, by understanding place value, how this works?

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

 

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program
©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=195

Description of Levels

Close

❎

Level 1 - Collecting like terms when 1 term is repeated

Level 2 - Collecting like terms when 2 terms are repeated

Level 3 - Multiplying a single positive integer over a bracket

Level 4 - Multiplying a single negative integer over a bracket

Level 5 - Multiplying a variable over a bracket

Level 6 - Expanding products of two simple binomials

Level 7 - Expanding products of two binomials

Level 8 - Squaring a binomial

Level 9 - Simplifying more complex expressions involving brackets

Level 10 - Expanding products of three binomials (cubic expressions)

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Binomial Theorem - Exercises in expanding powers of binomial expressions and finding specific coefficients.

More Algebra - There are many more exercise, Starters and other Algebra resources on the main Algebra page.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Example

This program checks your answers by matching the text you have typed in with the text it has as the correct answer. For that reason it does not recognise equivalent correct answers. For example the expansion of 3(2a+7) can be written as 6a+21 or 21+6a but the program only recognises the first option as the correct answer. Please type in your answers so that the terms are in order of decreasing powers of the variable.

Level 1 example: 5d - (2d + 2)

Remove the brackets to give 5d - 2d - 2
[note that everything inside the bracket is subtracted from 5d]
Collect like terms to give 3d - 2

Level 2 example: (9d - 7) - (5d - 2)

Remove the brackets to give 9d - 7 - 5d + 2
[note that negative 2 becomes positive due to the negative sign in front of the second bracket]
Collect like terms to give 4d - 5

Level 3 example: 4(2d + 4)

Multiply each term inside the bracket by 4 to give 8d + 16

Level 4 example: -5(5d + 4)

Multiply each term inside the bracket by negative 5 to give -25d - 20

Level 5 example: 4d(5d - 5)

Multiply each term inside the bracket by 4d to give 20d^2 - 20d

Level 6 example: (d + 7)(d - 2)

Multiply each term of the first bracket by each term of the second bracket to give d^2 + 7d - 2d - 14
Collect like terms to give d^2 + 5d - 14

F.O.I.L. First Outer Inner Last

Level 7 example: (4d + 7)(3d + 2)

Multiply each term of the first bracket by each term of the second bracket to give 12d^2 + 8d + 21d + 14
Collect like terms to give 12d^2 + 29d + 14

Level 8 example: (3d + 2)^2

Write as (3d + 2)(3d + 2) then expand as in the previous example to give 9d^2 + 12d + 4

Level 9 example: 5(3d+1)-2(1-2d)

Multiply out the brackets to give 15d + 5 - 2 + 4d
Collect like terms to give 19d + 3

Level 10 example: (x+1)(2x-4)(x+2)

Multiply out the first pair of brackets to give (2x^2+2x-4)(x+2)
Multiply each term in the first set of brackets by each of the terms in the second set of brackets then collect like terms to give 2x3 + 6x^2 - 8

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

MathQuill Animation

Close

❎