The Lesson
Like terms can be subtracted. Imagine we wanted to subtract xy from 3xy.How to Add Like Terms in Algebra
Subtracting like terms is easy. Subtract the coefficients of the like terms from each other.Question
Subtract the like terms below from each other.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.
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
Subtract the coefficients from each other.
4
Make the number found in Step 3 (2) the coefficient of the term (xy).
Answer:
We have subtracted the like terms from each other:
3xy − xy = 2xy
How to Subtract 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
Subtract the like terms below from each other.Step-by-Step:
1
Check that the terms 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
Subtract the coefficients from each other.
4
Make the term found in Step 3 (a − b) the coefficient of the term (xy).
Answer:
We have subtacted the like terms from each other:
axy − bxy = (a − b)xy
Real Examples of How to Subtract Like Terms in Algebra
More examples of how to subtract like terms in algebra are given below.Can you see that the coefficients have been subtracted in each case?