# How To Simplify Terms In A Mathematical Expression. Algebra Help And Advice

If you are asked to simplify a mathematic expression then you need to write the expression in a shorter way (you are not working out the value of x!). Here are two important rules to clear in your head:

y + y = 2y – since 1y + 1y = 2y

y × y = y² - since multiplying a value by itself is called squaring

You can develop these rules a little further:

y + y + y = 3y

y × y × y = y³

And so on...

Another important rule when simplifying expressions is that you can only add or subtract like terms. So you can only add x terms to x terms, y terms to y terms, d² terms to d² terms etc...

Let’s take a look at some examples putting these rules into practice.

The first 3 examples involve adding and subtracting terms.

**Example 1**

Simplify this expression:

x + 5y + x + 3y

x + x can be simplified to 2x

5y + 3y can be simplified to 8y

This gives a final answer of 2x + 8y. Don’t be tempted to simplify this expression any further as they are different types of terms.

**Example 2**

Simplify this expression.

7x - 3y + 7y – 9x

Here you will have to competent with your negative numbers:

7x - 9x can be simplified to -2x

-3y + 7y can be simplified to 4y

This gives a final answer of -2x + 4y. Again, don’t be tempted to simplify this expression any further as they are different types of terms.

**Example 3 **

Simplify this expression.

4c + e – 10c + 3e

Here you will have to competent with your negative numbers:

4c – 10c can be simplified to -6c

e + 3e can be simplified to 4e

This gives a final answer of –6c + 4e.

The next couple of examples involve multiplying terms (not adding terms). These are done in a slightly different way. The answer will have the number at the start followed by the letters in alphabetical order.

**Example 4**

Simplify this expression.

5y × 3y

This time the terms are being multiplied. When multiplying put the letters in alphabetical order and have the number at the start of the term

5 × 3 = 15

y × y = y²

15y²

**Example 5**

Simplify this expression.

4k × 7km

This time the terms are being multiplied. When multiplying put the letters in alphabetical order and have the number at the start of the term

4 × 7 = 28

k × km = k²m

So the final expression will be 28k²m

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