simplifying expressions

Collecting like terms

To simplify an expression, we use like terms.

Look at the expression:

To simplify:

• The terms can be collected together to give .
• The numbers can be collected together to give .

So simplified is .

Notice that terms are separated by + and - signs, and these are always attached to the front of a term.

Question

Simplify this expression:

A Hide answer

To work it out:

• Write down the expression
• 

• Collect all the terms together which are alike. Remember that each term comes with an operation (+, -) which goes before it.
• 

• Simplify the terms.
• 

• Simplify the numbers separately.
• 

Answer: can be simplified to

Using formulae

We have already seen that and are examples of formulae. There are many others that we use regularly in other subjects. Sometimes we have to construct our own formula:

Example

A taxi firm charges per mile plus a fixed charge of . Write down a formula for the cost of hiring this taxi to travel miles.

Solution

• It costs to travel mile.
• It costs to travel miles.
• It costs to travel miles.

So traveling for miles will cost .

The formula is .

Note: .