Brackets :: Level 5Expand algebraic expressions containing brackets and simplify the resulting expression in this self marking exercise. 
This is level 5: multiplying a variable over a bracket. You can earn a trophy if you get at least 9 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 the [²] button to insert a power of 2 into your answer .
This is Brackets level 5. You can also try:
Level 1
Level 2
Level 3
Level 4
Level 6
Level 7
Level 8
Level 9
Level 10
Factorising
Collecting Like Terms
More Algebra
InstructionsTry 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. 



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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 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School: "What a brilliant website. We have just started to use the 'starteroftheday' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources online we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun." 


AnswersThere 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 adfree 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 MathsLearning 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 MapAre 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. TeachersIf 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: 

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/software/SW/Starter_of_the_day/Students/Brackets.asp?Level=5
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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)
More Algebra  There are many more exercise, Starters and other Algebra resources on the main Algebra page.
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
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
Multiply each term inside the bracket by 4 to give 8d + 16
Multiply each term inside the bracket by negative 5 to give 25d  20
Multiply each term inside the bracket by 4d to give 20d²  20d
Multiply each term of the first bracket by each term of the second bracket to give d² + 7d  2d  14
Collect like terms to give d² + 5d  14
F.O.I.L. First Outer Inner Last
Multiply each term of the first bracket by each term of the second bracket to give 12d² + 8d + 21d + 14
Collect like terms to give 12d² + 29d + 14
Write as (3d + 2)(3d + 2) then expand as in the previous example to give 9d² + 12d + 4
Multiply out the brackets to give 15d + 5  2 + 4d
Collect like terms to give 19d + 3
Multiply out the first pair of brackets to give (2x²+2x4)(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 2x^{3} + 6x²  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.
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.
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