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Like Terms

Like Terms

Terms which have the same variables and corresponding powers and/or roots. Like terms can be combined using addition an subtraction. Terms that are not like cannot be combined using addition or subtraction.

 

Example:     5x2y and 8x2y are like terms.

                   5x2y + 8x2y simplifies to 13x2y
                   5x2y – 8x2y simplifies to –3x2y

 

 

See also

FOIL method

Worked Example

Problem: Simplify the expression 7x²y − 3xy + 2x²y + 9xy − 4.
Step 1: Identify the like terms. Look for terms that share the same variable part (same variables with the same exponents).
7x2y and 2x2y(both have x2y)7x^2y \text{ and } 2x^2y \quad\text{(both have } x^2y\text{)}
Step 2: Identify the next group of like terms.
−3xy and 9xy(both have xy)-3xy \text{ and } 9xy \quad\text{(both have } xy\text{)}
Step 3: Note that −4 is a constant term with no matching like term, so it stays as is.
−4(constant)-4 \quad\text{(constant)}
Step 4: Combine each group of like terms by adding their coefficients.
7x2y+2x2y=9x2y7x^2y + 2x^2y = 9x^2y
Step 5: Combine the second group.
−3xy+9xy=6xy-3xy + 9xy = 6xy
Step 6: Write the simplified expression with all combined terms.
9x2y+6xy−49x^2y + 6xy - 4
Answer: The simplified expression is 9x2y+6xy−49x^2y + 6xy - 4.

Another Example

Problem: Are the terms 4x³ and 4x² like terms?
Step 1: Compare the variable parts. The first term has x raised to the 3rd power; the second has x raised to the 2nd power.
x3≠x2x^3 \neq x^2
Step 2: Since the exponents on x are different, these are NOT like terms, even though the coefficients are both 4 and the variable is the same letter.
Answer: No. 4x34x^3 and 4x24x^2 are not like terms because the exponents on xx are different. They cannot be combined.

Frequently Asked Questions

How do you know if two terms are like terms?
Check that they contain the exact same variables, each raised to the exact same exponent. The coefficients (the numbers in front) can be different — only the variable parts must match. For example, 3a2b3a^2b and −10a2b-10a^2b are like terms, but 3a2b3a^2b and 3ab23ab^2 are not because the exponents are distributed differently.
Are constants like terms with each other?
Yes. Constants such as 5, −2, and 100 are all like terms because none of them contain a variable. You can think of them as all sharing the same (empty) variable part. So 5+(−2)+1005 + (-2) + 100 simplifies to 103103.

Like Terms vs. Unlike Terms

Like terms share identical variable parts (same variables, same exponents) and can be combined through addition or subtraction. Unlike terms have different variable parts — for instance, 3x3x and 3x23x^2, or 5a5a and 5b5b — and cannot be combined. You can multiply or divide unlike terms, but you cannot add or subtract them into a single term.

Why It Matters

Combining like terms is one of the most frequently used steps in algebra. Every time you simplify an expression, solve an equation, or expand a product using the distributive property or FOIL, you finish by collecting like terms. Mastering this skill makes factoring, solving systems of equations, and working with polynomials far more manageable.

Common Mistakes

Mistake: Treating terms with the same variable but different exponents as like terms, such as combining 5x5x and 3x23x^2 into 8x28x^2 or 8x38x^3.
Correction: The exponents must match exactly. 5x5x has x1x^1 and 3x23x^2 has x2x^2, so they are unlike terms and cannot be combined.
Mistake: Combining the coefficients and also changing the variable part, such as writing 4x+5x=9x24x + 5x = 9x^2.
Correction: When you combine like terms, only the coefficient changes. The variable part stays the same. The correct result is 4x+5x=9x4x + 5x = 9x.

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