How to Add Like Terms in Algebra
Adding Like Terms in Algebra
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.
StepbyStep:
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.
StepbyStep:
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?