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Here we will learn about simplifying algebraic expressions by **collecting like terms**.

There are also collecting like terms worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Collecting like terms** is a way of simplifying algebraic expressions. It is also known as combining like terms.

To do this we identify the like terms in an algebraic expression and combine them by adding or subtracting.

**See also:** Simplifying expressions

E.g.

This is an expression with

\[3a +4b + 2a -2b\]

** 3a **and

The

\[\begin{align*}
3a +4b + 2a – b &= 3a + 2a+ 4b – b\\
&=5a+2b\\
\end{align*}\]

This expression cannot be simplified any more as the

In order to simplify algebraic expressions by collecting like terms:

**Identify the like terms****Group the like terms****Combine the like terms by adding or subtracting**

Get your free Collecting like terms worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONGet your free Collecting like terms worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOONSimplify:

\[ 3x+2x +4x \]

**Identify the like terms**

All the terms involve an

\[ 3x+2x +4x \]

2**Group the like terms**

The like terms are already grouped together.

\[3x+2x +4x \]

3**Combine the like terms by adding or subtracting**

\[3x+2x +4x =9x\]

The final answer is

\[9x\]

Simplify:

\[ 6a-3a +4a \]

**Identify the like terms**

All the terms involve an

\[ 6a-3a +4a\]

**Group the like terms**

The like terms are already grouped together.

\[6a-3a +4a \]

**Combine the like terms by adding or subtracting**

\[6a-3a +4a=7a \]

Because

\[6-3+4=7\]

The final answer is:

\[7a\]

Simplify:

\[7a+4b+2a+3b\]

**Identify the like terms**

The terms involving **7a****+2a**

The terms involving **+4b****+3b**

The plus (or minus) sign belongs to the term after it.

**Group the like terms**

\[7a+4b+2a+3b=7a+2a+4b+3b\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
7a+4b+2a+3b &=7a+2a+4b+3b\\
&=9a+7b\\
\end{align*}\]

Because

\[7+2=9\]

And

\[4+3=7\]

The final answer is:

\[9a+7b\]

Simplify the linear expression:

\[5x+4y-3x+5y\]

**Identify the like terms**

The terms involving **5x****-3x**

The terms involving **+4y****+5y**

The plus or minus sign belongs to the term after it.

**Group the like terms**

\[5x+4y-3x+5y=5x-3x+4y+5y\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
5x+4y-3x+5y &=5x-3x+4y+5y\\
&=2x+9y\\
\end{align*}\]

Because

\[5-3=2\]

And

\[4+5=9\]

The final answer is

\[2x+9y\]

Simplify the algebraic terms:

\[2c-5d+4+3c+7b+2\]

**Identify the like terms**

The terms involving **2c****+3c**

The terms involving **-5b****+7b**

The terms that are only numbers are known as constants (**+4****+2**

The plus or minus sign belongs to the term after it.

**Group the like terms**

\[ 2c-5d+4+3c+7d+2= 2c+3c-5d+7d+4+2\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
2c-5d+4+3c+7d+2 &=2c+3c-5d+7d+4+2\\
&=5c+2d+6\\
\end{align*}\]

Because

\[2+3=5\]

And

\[-5+7=2\]

And

\[4+2=6\]

The final answer is

\[5c+2d+6\]

Simplify:

\[-6x+5y+4+2x-3y-7\]

**Identify the like terms**

The terms involving **-6x****+2x**

The terms involving **5y****-3y**

The terms that are only numbers are known as constants (**+4****-7**

The plus or minus sign belongs to the term after it.

**Group the like terms**

\[ -6x+5y+4+2x-2y-7= -6x+2x+5y-2y+4-7\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
-6x+5y+4+2x-2y-7 &=-6x+2x+5y-2y+4-7\\
&=-4x+3y-3\\
\end{align*}\]

Because

\[-6+2=-4\]

And

\[5-2=3\]

And

\[4-7=-3\]

The final answer is

\[-4x+3y-3\]

Simplify:

\[8x^{2}+5x-4x^{2}+7x\]

**Identify the like terms**

The terms involving ^{2}**+8x****-4x**

The terms involving **+5x****+7x**

The plus or minus sign belongs to the term after it.

**Group the like terms**

\[8x^{2}+5x-4x^{2}+7x = 8x^{2}-4x^{2}+5x+7x\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
8x^{2}+5x-4x^{2}+7x &= 8x^{2}-4x^{2}+5x+7x\\
&=4x^{2}+12x\\
\end{align*}\]

Because

\[8-4=4\]

And

\[5+7=12\]

The final answer is

\[4x^{2}+12x\]

Simplify:

\[6x^{2}y-2x^{2}+4x^{2}y-5x^{2}\]

**Identify the like terms**

The terms involving ^{2}y**+6x****y****-4x****y**

The terms involving ^{2}**-2x****-5x**

The plus or minus sign belongs to the term after it.

**Group the like terms**

\[6x^{2}y-2x^{2}+4x^{2}y-5x^{2}=6x^{2}y+4x^{2}y-2x^{2}-5x^{2}\]

**Combine the like terms by adding or subtracting**

\[\begin{align*}
6x^{2}y-2x^{2}+4x^{2}y-5x^{2}&=6x^{2}y+4x^{2}y-2x^{2}-5x^{2}\\
&=10x^{2}y-7x^{2}\\
\end{align*}\]

Because

\[6+4=10\]

And

\[-2-5=-7\]

The final answer is

\[10x^{2}y-7x^{2}\]

**No coefficient (number) seen in front of a term**

If there is no coefficient (number) seen in front of a term then the coefficient is

\[x+4x=1x+4x=5x\]

**When asked to simplify an algebraic expression it is possible for the answer to be zero**

It is possible for all the terms to be cancelled out and the answer is zero.

E.g.

\[5x+3y-5x+4y=7y\]

The terms involving

**Terms must be exactly the same to be “like terms”**

Terms involving ^{2}

\[3y+4y^2+2y=5y+4y^2\]

This has been simplified as far as possible.

**The order of the terms in the final answer is not important**

The order of the terms is not critical as long as the plus and minus signs are with the correct term.

So:

\[3m+4n=4n+3m\]

And:

\[-2x+5y=5y-2x\]

1. Simplify:

4x+2x+3x

9x

11x

8x

9xxx

4x+2x+3x=9x

Because:

4+2+3=92. Simplify:

3a-2a+4a

5a^3

9a^3

9a

5a

3a-2a+4a=5a

Because:

3-2+4=53. Simplify:

5c+3d-2c+4d

7c+7d

3c+7d

7c-d

10cd

\begin{aligned}
5c+3d-2c+4d &=5c-2c+3d+4d\\
&=3c+7d\\
\end{aligned}

4. Simplify:

7x-2y-4x+5y

3x+3y

11x+7y

3x+7y

6xy

\begin{aligned}
7x-2y-4x+5y &=7x-4x-2y+5y\\
&=3x+3y\\
\end{aligned}

5. Simplify:

2m+3n+1+4m+5n+6

5m+5n+11

6m+8n+7

21mn

5m+7n+7

\begin{aligned}
2m+3n+1+4m+5n+6 &=2m+3n+1+4m+5n+6\\
&=6m+8n+7\\
\end{aligned}

6. Simplify:

6p-4q+5-2p+2q+3

4p+6q+8

8p+6q+8

4p-2q+8

8p-2q+8

\begin{aligned}
6p-4q+5-2p+2q+3 &=6p-2p-4q+2q+5+3\\
&=4p-2q+8\\
\end{aligned}

1. Simplify: 9a-4a+3a

**(1 mark)**

Show answer

8a i

**(1)**

2. Simplify: 7x+5y-2x+3y

**(2 marks)**

Show answer

for either 5x or 8y

**(1)**

5x+8y i

**(1)**

3. The diagram shows a pentagon. It has one line of symmetry.

AE = 5x

AB = 2x+3

BC = x+2

Write an expression for the perimeter in its simplest form.

**(3 marks)**

Show answer

CD = x+2

DE = 2x+3

for using symmetry to find one of the sides CD or DE

**(1)**

Perimeter is: 5x+2x+3+x+2+2x+3+x+2

for adding the 5 sides together

**(1)**

for simplifying and writing the final answer: 11x+10

**(1)**

You have now learned how to:

- Simplify algebraic expressions by collecting like terms

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