Collecting like terms
Combine repeated quantities without confusing different variables or powers.
Before you begin
- Coefficients and terms
- The distributive property
Look for the same variable part
Like terms have the same variable part, including the same powers. Three lots of x and two lots of x make five lots of x: 3x + 2x = 5x. But x and x² describe different quantities, so they cannot be combined this way. Constants are like terms with one another. Identify the full term, including its sign, before grouping.
Explain the combined coefficient
Collecting terms is the distributive property in reverse: 3x + 2x = (3 + 2)x. Addition changes the coefficient, not the exponent. Keep unlike terms separate and preserve the operation signs. Substitute a simple value into the original and simplified expressions as an error check, while remembering that agreement at one value alone is not a proof of equivalence.
Worked example
Simplify 4x + 3 + 2x + 5.
Show the worked solution
- Group the terms containing x: 4x + 2x = 6x.
- Group the constants: 3 + 5 = 8.
- Combine the two groups as 6x + 8. At x = 2 both forms equal 20.
6x + 8.
Try it yourself
Which expression is equivalent to y + y + y?
Common mistakes
- x + x is 2x, whereas x × x is x².
- Unlike variable parts cannot be collected as one term.
What can you explain now?
Simplify 7a + 2b + 3a + 4b and explain why two terms remain.
Compare with the explanation
10a + 6b.
Combine the a terms and the b terms separately. Without a relationship between a and b, their values cannot be treated as identical quantities.
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Common Core mathematics standards ↗