Collecting Like Terms | Maths Made Easy

# Collecting Like Terms

Level 1 Level 2 Level 3

## What you need to know

### Collecting Like Terms

To be able to collect like terms, there are 3 things we need to answer first

• What is a term?
• What is a like term?
• How do we collect them?

A term can come in three forms:

• A number by itself
• A letter by itself
• A combination of letters and numbers

Like terms have the same combination of letters and numbers. To add or subtract terms with the same letter, we add or subtract the numbers like usual and just put the letter back on the end.

### Collecting Like Terms

Questions and expressions aren’t always linear, they could have powers like this:

They could also have more than one letter, like this:

Note:A common mistake is to think that when you add algebraic terms together they will become squared, so try saying it like this: “I have four $x$s, I add two more to give me six, and then take one away. Now I have 5$x$s.”

### Like Terms With Different Letters

They might even have these letters combined together, like this:

Finally, they might even have a combination of all of these!

### Example 1: Collecting Like Terms

Collect the like terms in the following expression:

$$4x+2x+3-x+1$$

Firstly identify the like terms.

You then need to collect the like terms

And now you just need to do the additions and subtractions as usual.

$$4x+2x+3-x+1=5x+3$$

### Example Questions

It is often easier to first group the similar terms together, before simplifying,

\begin{aligned}5x+5-2x+3-4-x &=(5x-2x-x)+(5+3-4) \\ &=2x+4\end{aligned}

It is often easier to first group the similar terms together, before simplifying,

\begin{aligned}ab+bc+2ab-bc+a &= a+(ab+2ab)+(bc-bc) \\ &=a+3ab \end{aligned}

It is often easier to first group the similar terms together, before simplifying:

\begin{aligned}11x+7y-2x-13y &= (11x-2x)+(7y-13y) \\ &=9x-6y \end{aligned}

It is often easier to first group the similar terms together, before simplifying:

\begin{aligned}2m+6n-3+8n+5n &= (2m+5m)+(6n+8n)-3 \\ &=7m+14n-3 \end{aligned}

It is often easier to first group the similar terms together, before simplifying:

\begin{aligned}2a^2 + 5b-2a -3b+5a^2&= (2a^2+5a^2)+(5b-3b)-2a \\ &=7a^2+2b-2a\end{aligned}

Level 1-3

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