How to Expand Brackets

Expanding brackets is an algebraic technique used when solving equations 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.

The image below shows the expression 2(x + 8) and 6y(9 - y). The answer is 2x + 16 and 54y - 6y².

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. a multiplied by a is a². Next b multiplied by a is ab, and a multiplied by - b is - ab. Finally b multiplied by -b equals - b². The answer is a² - b².

What Is The Meaning of Brackets?

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. First multiply 4 by 3x. The answer is 12x. Next multiply 4 by - 5. The answer is - 20. 12x - 2x equal 10x. When simplified the answer is 10x - 20.

The second image shows 8(y - 7) + 5(y - 2), when simplified the answer is 13y - 66.