Like Terms
In short: Like terms are terms whose variable parts match exactly, such as 8x and -3x, so their coefficients can be added or subtracted to combine them.
6th GradeAlgebra6.EE.A.3
What is Like Terms?
Like terms name the same kind of thing, so their amounts can be merged. You can add 8 apples and 3 apples into one total, but not 8 apples and 3 oranges.
Precisely, terms are alike when they have the same variables raised to the same powers; only the coefficients may differ. So \(8x\) and \(-3x\) combine to \(5x\), while \(8x\) and \(8x^2\) do not, and constants like 4 and 11 are like each other.
How to spot it
- An expression has several pieces with the same letter, like 7m + 2 + 5m.
- A question asks you to simplify or to write an expression with fewer terms.
- Perimeters of shapes with variable sides add several pieces of the same length.
- Pieces with different letters or powers, such as 3a and 3b, sit side by side.
The method
- Underline or color the terms that share the same variable part, and treat constants as one family.
- Group each family together, keeping the sign that sits in front of every term.
- Add or subtract the coefficients in each family and keep the variable part unchanged.
- Write the result and check by substituting a small number for the variable on both sides.
Like Terms: solved example
Problem
Simplify \(9a + 4b – 3a + 10 + b – 7\).
Solution
Group the families: a-terms \(9a – 3a = 6a\); b-terms \(4b + b = 5b\); constants \(10 – 7 = 3\).
The simplified expression is \(6a + 5b + 3\). Check with \(a = 1\) and \(b = 1\): the original gives 14 and so does the result.
Try it
Question 1
Combine \(15y – 22y + 4\).
Show the answer
\(15y – 22y = -7y\), so the answer is \(-7y + 4\).
Question 2
Can \(5x^2\) and \(5x\) be combined? Why or why not?
Show the answer
No. The powers of x differ, so they are not alike, and \(5x^2 + 5x\) stays as written.
Like Terms vs. Equivalent Expressions
Combining like terms is one technique, a way of shortening an expression. Equivalent expressions is the bigger idea: two expressions that always give the same value, whether you got there by combining, distributing or rearranging.
Keep going
Lessons
Worksheets and quizzes
- Equivalent Expressions and the Distributive Property – Worksheet
- Equivalent Expressions and the Distributive Property – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Algebra