# How to simplify algebraic expressions.

Goal:

## Theory:

Part 1

Algebraic expressions contain alphabetic symbols as well as numbers. When an algebraic expression is simplified, an equivalent expression is found that is simpler than the original. This usually means that the simplified expression is smaller than the original.

There is no standard procedure for simplifying all algebraic expressions because there are so many different kinds of expressions, but they can be grouped into three types:

(a) those that can be simplified immediately without any preparation.

(b) those that require preparation before being simplified.

(c) those that cannot be simplified at all.

NOTE: This article will discuss three examples of algebraic expressions that can be simplified immediately.

##### Example 1:

2x + 3y – 2 + 3x + 6y + 7

This expression can be simplified by identifying like terms and then grouping and combining like terms, like this:

• +2x and +3x are like terms, and can be combined to give +5x,
• +3y and +6y combine to give +9y, and
• -2 and +7 combine to give +5.

So after simplifying, this expression becomes:

5x + 9y + 5

##### Example 2:

3b – (4b – 6b + 2) + b

There is a minus sign before the left bracket, so the sign of each term inside the brackets will change when the brackets are removed:

• Removing the brackets:

NOTE: This step is not displayed by Algematics unless you use the expand command as explained in the method section below.

3b + 2b – 2 + b

• Grouping and combining the like terms: +3b, +2b and +b combine to give 6b:

6b – 2

##### Example 3: Expressions that are products and quotients of simple factors that include powers with the same base can be simplified immediately by adding and subtracting the indices of the powers.

This expression simplifies to give: 4p²q³

## Method:

Part 2

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’.

We will use Algematics to simplify each of the example expressions above. Then you will be able to simplify similar expressions yourself.

##### Step 1 Enter the data

Click and type your 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…

2x + 3y – 2 + 3x + 6y + 7

and then click You will enter the quadratic formula twice, once with a plus sign and once with a minus sign.

##### Step 2, Use the Simplify command

Click (simplify) repeatedly until the expression is completely simplified.

If the expression is not changed by the simplify command, then either it is completely simplified, or you need to use another approach.

NOTE: If you simplify two many times, you will duplicate the last step. You can delete a duplicate step by selecting it, then using Ctrl+Delete on the keyboard.

To display a step where brackets are removed, as for example 2 above, click (expand).

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