Subtraction of Like and Unlike Terms

The subtraction of terms in algebra follows similar principles to addition, but with an added twist of changing signs. The subtraction of like and unlike terms has specific rules that must be followed to simplify algebraic expressions effectively.

• Subtraction of Like Terms: Like terms have the same variables and powers. The subtraction of like terms involves subtracting their coefficients.

• Subtraction of Unlike Terms: Unlike terms have different variables or different powers. These terms cannot be combined into a single term, but they can be written as an expression with a subtraction sign between them.

Identify Like Terms:

• Like terms have the same variable(s) and the same power(s).

Change the Sign of the Subtracted Term:

• In subtraction, the sign of the term being subtracted is changed.

Subtract the Coefficients:

• Subtract the numerical coefficients of like terms, while keeping the variable part the same.

• Example 1:

  4x - 2x = (4 - 2)x = 2x

• Example 2:

  -4x + 2x = (-4 + 2)x = -2x

• Example 3:

  3x - 7x = (3-7)x = -4x

• Example 4:

  6ab + 3ab − 4ab

  = (6ab + 3ab) - 4ab

  = 9ab - 4ab = 5ab

Identify Unlike Terms:

• Unlike terms do not have the same variables or powers.

Cannot Combine to a Single Term:

• The subtraction of unlike terms does not result in a single simplified term. They can only be written together as an expression with the subtraction sign.

• Example 1:

  $2ab-4bc(Cannot\; be\; combined)$

  The result is: 2ab − 4bc

• Example 2:

  $4ab-2bc(Cannot\; be\; combined)$

  The result is: 4ab − 2bc

• Like terms have the same variables with the same powers

• Only like terms can be subtracted to form a single term

• Subtract the coefficients and keep the variable part unchanged

• Unlike terms cannot be combined into a single term

Common Mistakes to Avoid

•  Don't combine unlike terms: 3x + 5y ≠ 8xy
• Watch the signs carefully: 7x - (-3x) = 7x + 3x = 10x
• Keep the variable part unchanged: 5a - 2a = 3a (not 3)