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Combining Like Terms

In this lesson you’ll learn what “like terms” are and how to combine them to simplify algebraic expressions.

Like terms have the same variable raised to the same power (e.g., 5x5x and 3x3x, or 77 and 22, since constants are like terms with no variable).

To combine like terms: Add or subtract their coefficients, keep the variable the same.

Examples:

  • 5x+3x=8x5x + 3x = 8x
  • 12y7y=5y12y - 7y = 5y
  • 4+92=114 + 9 - 2 = 11 (constants only)
  • 6a+2b4a+5b=(6a4a)+(2b+5b)=2a+7b6a + 2b - 4a + 5b = (6a - 4a) + (2b + 5b) = 2a + 7b

Only combine terms that match exactly. 3x3x and 3x23x^2 are not like terms.

Simplify 7x+4+2x9+5y7x + 4 + 2x - 9 + 5y

  1. Group like terms: (7x+2x)+5y+(49)(7x + 2x) + 5y + (4 - 9)
  2. Combine: 9x+5y59x + 5y - 5

Final simplified expression: 9x+5y59x + 5y - 5

Combining like terms helps simplify real costs or totals. Example: Weekly expenses = 45 dollars food + 30 dollars gas + 15 dollars snacks + 20 dollars coffee. Group: (45 + 15) food/snacks + 30 gas + 20 coffee = 60 dollars food/snacks + 30 gas + 20 coffee. Or total pay = 18 dollars/hour × h hours + 50 dollars bonus. Leave as is, but if multiple rates, combine like terms.

Simplify $6x + 4x$.
Combine $9y - 5y + 3$.
Simplify $2a + 7b - a + 3b$.
A bill has 35 dollars fixed + 12 dollars per hour for 3 hours + 8 dollars fee. Simplified total?
Simplify $5x + 3 - 2x + 7 - x$.