Theory:

Terms which have the same variables and powers are like terms.
Example:
  • \(8xy²\) and \(−5xy²\) are like terms because they have the same variable \(xy^2\).
  • \(2x^2y\), \(3x^2y\), \(4x^2y\), \(5x^2y\) and \(6x^2y\) are like terms because they have the same variable \(x^2y\).
  • \(3a^2bc\), \(- a^2bc\) and \(-4 a^2bc\) are like terms because they have the same variable \(a^2bc\).
Important!
Coefficients need not to be same in like terms.
Terms that do not have the same variables or powers are unlike terms.
Example:
  • \(3abc\) and \(3xyz\) are unlike terms because they have different variables such as \(abc\) and \(xyz\).
  • \(2x^2y\), \(3a^3b\), \(4pq\), \(5r^4s\) and \(6d^5e\) are unlike terms because they have different variables such as \(x^2y\), \(a^3b\), \(r^4s\) and \(d^5e\).
  • \(3a^2bc\), \(- x^3yz\) and \(-4 pqr\) are unlike terms because they have different variables such as \(a^2bc\), \(- x^3yz\) and \(pqr\).