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# Adding Like Terms in Algebra

(KS3, Year 7)

## The Lesson

Like terms can be added. Imagine we wanted to add**3xy**and

**xy**.

## How to Add Like Terms in Algebra

Adding like terms is easy. Add the coefficients of the like terms together.## Question

Add the like terms below together.## Step-by-Step:

# 1

Check that the terms are like terms.

**3xy**and**xy**are like terms.-
They have the same variables:
**x**and**y**. -
Each variable has the same exponent:
**x**and**y**both have no exponents (actually an explicit exponent of 1). -
The only difference is the coefficient:
**3xy**has a coefficient of**3**,**xy**has no coefficient (actually an explicit coefficient of 1).

# 2

Identify the coefficients of the like terms.

**Don't forget:**A coefficient is the constant (usually a number) in front of a term. If a letter does not have a number in front of it, its coefficient is**1**.# 3

Add the coefficients together.

# 4

Make the number found in

**Step 3**(4) the coefficient of the term (xy).## Answer:

We have added the like terms together:**3xy**+

**xy**=

**4xy**

## How to Add Like Terms in Algebra When the Coefficients Are Letters

Coefficients can be letters as well as numbers. By convention, the letters**a**,

**b**,

**c**are used to represent constants (such as coefficients) whereas

**x**,

**y**,

**z**are used for variables.

## Question

Add the like terms below together.## Step-by-Step:

# 1

Check that the terms are like terms.

**axy**and**bxy**are like terms.-
They have the same variables:
**x**and**y**. -
Each variable has the same exponent:
**x**and**y**both have no exponents (actually an explicit exponent of 1). -
The only difference is the coefficient:
**axy**has a coefficient of**a**,**bxy**has a coefficient of**b**.

# 2

Identify the coefficients of the like terms.

# 3

Add the coefficients together.

# 4

Make the term found in

**Step 3**(a + b) the coefficient of the term (xy).## Answer:

We have added the like terms together:**axy**+

**bxy**=

**(a + b)xy**

## Real Examples of How to Add Like Terms in Algebra

More real examples of how to add like terms in algebra are given below:Can you see that the coefficients have been added in each case?

## What Is a Like Term in Algebra?

Like terms are terms with the same combination of letters (and/or brackets). The only difference is the sign or number in front of the group of letters. Each letter (and/or bracket) in a like term must have the same exponents - the number that sits to the top-right of the letter.## What Is a Term in Algebra?

A term is a collection of numbers, letters and brackets all multiplied together. Terms are separated by + or - signs in an algebraic expression.**Help Us To Improve Mathematics Monster**

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