Expand algebraic expressions with brackets.
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:
To 'expand' an expression means to remove the brackets.
Differences are expanded in the same way. For example, expanding this expression:
gives this expanded expression:
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:
+ 3ab - 5bc²
In this case, each term can then be simplified, giving:
6a²b²c + 9a²b³c
The following steps demonstrate how to expand bracketed expressions using Algematics.
Step 1Â Enter the expression to be expanded
Click Â 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
until the message: ‘INSERT’ appears. If
necessary, use the ‘ * ’ symbol for multiply, and the ‘ / ’ symbol for
Â Â Â Â Â Â
and then click
Step 2Â Expand the brackets
the first example, the expanded expression looks like this:
If necessary, click Â enough times to simplify the terms of the expanded expression.