Expand algebraic expressions containing brackets and simplify the resulting expressions.
This is level 4: multiplying a single negative integer over a bracket. 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 .
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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.
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 20d^2 - 20d
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
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
Write as (3d + 2)(3d + 2) then expand as in the previous example to give 9d^2 + 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 (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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