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Brackets

Expand algebraic expressions containing brackets and simplify the resulting expressions.
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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

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

☐ ✓ ✗

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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.
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Description of Levels

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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)

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.

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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.

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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

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