Algebraic Expressions (Two-step) • Topic 1 of 2

Combining Like Terms

Like terms have the same variable raised to the same power. Constants (plain numbers) are also like terms with each other.

ExpressionLike TermsUnlike Terms
4x + 2x4x and 2x (same variable)—
3x + 2y—3x and 2y (different variables)
5x^2 + 3x—5x^2 and 3x (different powers)

Rules for combining like terms:

  • Add or subtract the coefficients only
  • The variable part stays unchanged
  • Always carry the sign (+ or -) with each term
LIKE TERMS SORTING:

Expression: 4x + 2y - x + 3y

Step 1: Group like terms
  x-terms: 4x and -x
  y-terms: 2y and 3y

Step 2: Combine
  (4x - x) = 3x
  (2y + 3y) = 5y

Final Answer: 3x + 5y
Solved Examples
1
Worked Example
Simplify: 7a + 3b - 2a + 4b
SolutionGroup like terms: (7a - 2a) + (3b + 4b) = 5a + 7b
2
Worked Example
Simplify: 5x + 2 - 3x + 7
SolutionGroup like terms: (5x - 3x) + (2 + 7) = 2x + 9
3
Worked Example
Simplify: 4m - 2n + 3m + n - 5
Solution(4m + 3m) + (-2n + n) - 5 = 7m - n - 5

Key Points

  • Only like terms (same variable AND same exponent) can be combined
  • Add or subtract only the coefficients
  • The variable part does not change when combining
  • Always carry the sign with each term
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.$3x+2x=$
Explanation: Add coefficients of like terms.
Q2.Like terms have the same variable raised to the same:
Explanation: Same power.
Q3.$5a-2a=$
Explanation: $3a$.
Q4.$4x$ and $3y$ are:
Explanation: Different variables.
Practice more MCQs → 📝 Assignment · 35 marks