# 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.

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Colour the sweet wrappers so that no two are the same. A multi-level activity designed to encourage a systematic strategy for finding all of the different permutations.

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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.

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## Example

### 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

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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.

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