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This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to how to expand algebraic expressions with brackets.    (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Algematics software. Click here for instructions.

Theory:

When brackets are removed from around a sum or difference, then any factors outside the brackets must be multiplied by each term inside the brackets.

For example, to remove the brackets in this expression:

a(x + y)

the factor ‘a’ outside the brackets must be multiplied by both the ‘x’ and the ‘y’ inside the brackets, like this:

a´x + a´y

To 'expand' an expression means to remove the brackets.
During expansion, the factor ‘a’ is distributed over the terms ‘x’ and ‘y’.

Differences are expanded in the same way. For example, expanding this expression:

a(x - y)

gives this expanded expression:

a´x - a´y

If there are several factors outside the brackets, and more than two terms inside the brackets, then exactly the same procedure applies.

For example, expanding:

3ab²c(2a + 3ab - 5bc² + 1)

gives:

3ab²c´2a + 3ab²c´3ab - 3ab²c´5bc² + 3ab²c´1

In this case, each term can then be simplified, giving:

6a²b²c + 9a²b³c - 15ab³c³ + 3ab²c

Method:

IMPORTANT: This topic assumes that you know how to enter mathematical formulas into Algematics. Find out how by completing the three simple tutorials in the 'Getting Started' section of the Algematics program 'Help'.

The following steps demonstrate how to expand bracketed expressions using Algematics.

Step 1  Enter the expression to be expanded

Click  and type your the left hand expression into the maths box in the data entry dialog box.

If the ‘EMPTY’ message is not displayed between the blue buttons, click the  button until the message: ‘INSERT’ appears. If necessary, use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for divide.

       Maths...

 

and then click

Step 2  Expand the brackets

Click .

For the first example, the expanded expression looks like this:

ax + ay

If necessary, click  enough times to simplify the terms of the expanded expression.