Combining Like Terms

Terms that have the same variables raised to the same power are called “like terms”, where the numerical coefficients are different. Like terms are combined with each other to simplify the algebraic expressions. For example: 7x, 10x, and -2x are like terms. 3x2y, -5x2y and 13x2y are like terms. Now we can combine like terms by adding or subtracting them. For example: -15a + 7a + 6b – 3a + 8a – 20b Combining like terms we get, (-15 + 7 – 3 + 8)a + (6 – 20)b 8a – 14b Some facts about like terms:
  • 2 × a is the same as 2a and is easier to write it as “2a” when we simplify an expression.
  • 1 × b is the same as b.
  Check Point: Simplify the given expressions:
  1. 21 + 24r – 71 – 9r
  2. 13x + 5y – 8x – 12y + 20
  3. 5a – 15b + 20a + 18b + 3
  4. -2xy2 + 5xy + 7xy2 – 15xy + 20
  5. 20a2b + 30a – 7b – 10a2b – 12a – 3b
Answer key
  1. 15r – 50
  2. 5x – 7y + 20
  3. 25a + 3b + 3
  4. 5xy2 – 10xy + 20
  5. 10a2b + 18a – 10b