Algebra
Grade 2-4Collecting Like Terms
Collecting like terms means combining the parts of an expression that share the same letter and power, so that a longer expression can be written more simply. This lesson covers identifying like terms, simplifying expressions with one or two variables, and simplifying expressions that include powers such as x².
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Identifying like terms
Like terms have exactly the same letter raised to exactly the same power. Different letters, or the same letter raised to different powers, are not like terms and cannot be combined.
In the list 4a, 3b, 7a, 2c, the terms 4a and 7a are like terms, since they both involve a raised to the power 1. The terms 3b and 2c are not like terms as each other, or as the a terms.
Simplifying expressions with one variable
Add or subtract the coefficients of the like terms, keeping the letter the same, and keeping track of the sign in front of each term.
3a + 5a + 2a simplifies to 10a, since 3 + 5 + 2 = 10. For 7b − 2b + 3b, working left to right gives 7 − 2 + 3 = 8, so the answer is 8b.
Simplifying expressions with two variables
Group the terms by letter first, then collect each group separately, keeping any negative signs attached to the term they belong to.
3x + 2y + 5x − y has x-terms 3x + 5x = 8x, and y-terms 2y − y = y, giving a simplified expression of 8x + y.
Simplifying expressions with powers
Terms with a squared letter, such as x², are only like terms with other x² terms, never with plain x terms, so collect each power separately.
3x² + 2x − x² + 5x has x²-terms 3x² − x² = 2x², and x-terms 2x + 5x = 7x, giving a simplified expression of 2x² + 7x.
Worked Examples
Three exam-style questions, fully solved.
Simplify 3a + 5a + 2a.
Easy- 1.Add the coefficients of the like terms: 3 + 5 + 2
Answer: 10a
Simplify 3x + 2y + 5x − y.
Medium- 1.Collect the x-terms: 3x + 5x = 8x
- 2.Collect the y-terms: 2y − y = y
Answer: 8x + y
Simplify 3x² + 2x − x² + 5x.
Hard- 1.Collect the x²-terms: 3x² − x² = 2x²
- 2.Collect the x-terms: 2x + 5x = 7x
Answer: 2x² + 7x
Avoid These
The most common mistakes students make.
Combining terms that are not like terms, such as adding 4a and 3b together as if they were the same type of term.
Losing track of the sign in front of a term, especially when a subtraction appears partway through an expression or the terms are not already in order.
Combining x² terms with x terms, when they must be kept separate since they represent different powers of x.
Multiplying the letters together when combining like terms, instead of just adding or subtracting the coefficients and keeping the letter the same.
Forgetting a term entirely when there are several terms to collect, especially when the expression mixes two different letters.
FAQ
Questions parents and students ask.
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