# Collecting Like Terms

## Collecting Like Terms Revision

**Collecting Like Terms **

A **term** is an **individual part** of an expression and typically appears in one of three forms:

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

**Like terms** have the same combination of letters. 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.

**Skill 1: Linear Expressions with a Single Variable**

Linear expressions are those in which all variables (i.e. the letters) are to the **power of 1 ** so there are no squared or cubed terms.

**Example:** simplify the following,

2a + 3 + a + 5

We have to **group the terms that are similar**; all the terms that are just numbers need grouping together and simplifying, as do the similar algebraic terms.

This gives,

2a+1a = 3a

3 + 5 = 8

This gives the final answer to be,

2a + 3 + a + 5 = 3a + 8

Note: Normally the 1 in front of the a is left out but we have included it here to make it clear the steps being taken.

**Skill 2: Like Terms With Different Letters**

Sometimes terms have more than one variable (letter) multiplied or divided together:

\textcolor{red}{xy} + \textcolor{blue}{y} + \textcolor{red}{2xy}

in this instance, \textcolor{red}{xy} and \textcolor{red}{2xy}, are like terms that can be added together to simplify the expression, hence we find,

\textcolor{red}{3xy} + \textcolor{blue}{y}

**Skill 3: Identifying Like Terms with Powers**

Terms of certain powers have to be grouped with terms of the same power. Such terms can also include multiple letters and powers.

2\textcolor{red}{x^2y} + \textcolor{blue}{xy^2} + 3\textcolor{red}{x^2y} + 5\textcolor{blue}{xy^2} = 5\textcolor{red}{x^2y} + 6\textcolor{blue}{xy^2}

- 2\textcolor{red}{x^2y} and 3\textcolor{red}{x^2y} are like terms
- \textcolor{blue}{xy^2} and 5\textcolor{blue}{xy^2} are like terms

**Example 1: Two Variables**

Simplify the expression 3y+2x+4x-y.

**[1 mark]**

\textcolor{blue}{3y} and -\textcolor{blue}{y} are like terms

\textcolor{purple}{2x} and \textcolor{purple}{4x} are like terms

**Example 2: Including Powers**

Simplify the expression 4x^2 +2x +3x^2.

**[1 mark]**

\textcolor{limegreen}{4x^2} and \textcolor{limegreen}{3x^2} are like terms

\textcolor{purple}{2x} has no like terms

**Example 3: Multiple Letters**

Simplify the expression 5mn +3xy+mn+x.

**[1 mark]**

\textcolor{maroon}{5mn} and \textcolor{maroon}{mn} are like terms

\textcolor{blue}{3xy} and \textcolor{limegreen}{x} have **no other like terms**

**Example 4: Multiple Letters and Powers**

Simplify the expression 2m^2n+3mn+2m^2n.

**[1 mark]**

\textcolor{maroon}{2m^2n} and \textcolor{maroon}{2m^2n} are like terms

\textcolor{blue}{3mn} has **no like terms**

## Collecting Like Terms Example Questions

**Question 1:** Simplify the following expression by collecting like terms:

**[1 mark]**

5x+5-2x+3-4-x

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

5x+5-2x+3-4-x \\ =(5x-2x-x)+(5+3-4) \\ =2x+4

**Question 2:** Simplify the following expression by collecting like terms:

**[1 mark]**

ab+bc+2ab-bc+a

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

ab+bc+2ab-bc+a \\ = a+(ab+2ab)+(bc-bc) \\ = a+3ab

**Question 3:** Simplify the following expression by collecting like terms:

**[1 mark]**

11x+7y-2x-13y

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

11x+7y-2x-13y \\ = (11x-2x)+(7y-13y) \\ =9x-6y

**Question 4:** Simplify the following expression by collecting like terms:

**[1 mark]**

2m+6n-3+8n +5m

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

2m+6n-3+8n+5n \\ = (2m+5m)+(6n+8n)-3 \\ = 7m+14n-3

**Question 5:** Simplify the following expression by collecting like terms:

**[1 mark]**

2a^2 + 5b-2a -3b+5a^2

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

2a^2 + 5b-2a -3b+5a^2\\ = (2a^2+5a^2)+(5b-3b)-2a \\ =7a^2+2b-2a