Expanding Brackets Worksheets and Answers
Expanding Brackets Worksheet Practice
Expanding brackets worksheets for years 8, 9 and 10 working at grades 3 to grade 5 for 9-1 GCSE Maths. This section currently contains 6 expanding brackets worksheets. Expanding brackets worksheet 1 and expanding bracket worksheet 2 involve simple algebraic expressions. Expanding bracket worksheet 2 asks students to use a grid method and the grids are provided on the expanding brackets worksheet. Expanding brackets worksheet 3 involves expanding the bracket and then simplifying the expression. Expanding brackets worksheet 4 asks students to expand double brackets using a grid method. Expanding brackets worksheet 5 is a more traditional expanding bracket worksheet and it contains three sections which increase in difficulty. Expanding brackets worksheet 6 is a mixed exercise whereby students both factorise and expand brackets on a single maths worksheet.
How to Expand Brackets
Expanding brackets is an algebraic technique used when solving equatons and simplifying expressions. To expand the brackets is to multiply everything inside the brackets, ( ), by what's outside the bracket. For example: 2(x + 3) is 2 multiplied by x added to 2 multiplied by 3. The result is 2x + 6.
Sometimes we expand brackets and then simplify the expression. The image below shows the expression 12(4x + 8) - 6x. The answer is 42x + 96. The second image shows 7(a - 11) + 2(3 + a), when simplified the answer is 9a - 71.
There are four expanding brackets examples below showing 2(a + 4), 5(c + 12), 3(2x - 7), 6a(a - b). The answers are 2a + 8, 5c + 60, 6x - 21 and 6a2 - 6ab.
Expanding Brackets Tricks
When expanding brackets there are simple rules to follow, shown in the graph below.
How To Expand Brackets Using FOIL
The FOIL method is the most common way to expand double brackets. FOIL stands for multiply the first, the outer, the inner and the last. In the example below, x is the first term of both brackets, x and 5 are the outer terms, 8 and x are the inner terms, and 8 and 5 are the last numbers. x multiplied by x is x2. x multipled by 5 is 5x. 8 multiplied by x is 8x. 8 multipled by 5 is 40. The result is x2 + 5x + 8x + 40. When simplified the final answer is, x2 + 13x + 40 because 5x + 8x equals 13x.
Expanding and Simplifying Brackets
Brackets can be expanded and simplified, this involves collecting like terms. The first example shows 4(3x - 5) - 2x. When simplified the answer is 10x - 20. The second image shows 8(y - 7) + 5(y - 2), when simplified the answer is 13y - 66.