Transum Software

Brackets :: Level 7

Expand algebraic expressions containing brackets and simplify the resulting expression in this self marking exercise.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9 Level 10 Info Help

This is level 7: expanding products of two binomials. 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 .

\((4a + 3)(4a + 4)\)

Squared Correct Wrong

\((2b + 5)(2b + 2)\)

Squared Correct Wrong

\((2c + 6)(4c + 3)\)

Squared Correct Wrong

\((6d + 5)(5d + 2)\)

Squared Correct Wrong

\((6e - 6)(5e + 7)\)

Squared Correct Wrong

\((7f - 8)(7f - 4)\)

Squared Correct Wrong

\((6g + 3)(4g - 10)\)

Squared Correct Wrong

\((10h - 2)(5h + 10)\)

Squared Correct Wrong

\((7i - 4)(7i + 9)\)

Squared Correct Wrong

\((12j + 13)(2j - 10)\)

Squared Correct Wrong

\((8k - 10)(3k - 13)\)

Squared Correct Wrong

\((8m - 14)(10m + 15)\)

Squared Correct Wrong


This is Brackets level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 8 Level 9 Level 10 Factorising Collecting Like Terms More Algebra


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Description of Levels



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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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 20d² - 20d

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

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

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

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

Level 8 example: (3d + 2)²

Write as (3d + 2)(3d + 2) then expand as in the previous example to give 9d² + 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 (2x²+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 + 6x² - 8

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