Addition of Like and Unlike Terms

• Addition of Like Terms: Like terms are terms that have the same variables raised to the same powers. The process of adding like terms involves adding the coefficients of the terms.

• Addition of Unlike Terms: Unlike terms have different variables or powers. They cannot be added to form a single term. However, they can be written together in the form of an expression, with each term separated by a "+" or "-" sign.

• Step 1: Identify Like Terms
               2x,3x
• Step 2: Combine Coefficients
              (2 + 3)x
• Step 3: Simplify the Result
              5x

Example 1

3x + 5x
= (3 + 5)x
= 8x

Example 2

4y² + (–2y²)
= (4 – 2)y²
= 2y²

Example 3

2ab + 3ab + 5ab
= (2 + 3 + 5) ab
= 10ab

Example 4

• 7x + (–3x) = (7 – 3)x = 4x

• −3xy², −5xy², and −xy²  = (−3 − 5 − 1)xy²  = −9xy²

• (–3m) + (–2m) = (–3 – 2)m = –5m

Unlike Terms – Cannot Be Added

Unlike terms differ in letters or powers. They stay separate with + or – signs.

Examples:
3x + 4y → cannot combine → write as 3x + 4y

2a² + 5a b → write as 2a² + 5ab

2y³, −5xy and 3x³ → write as = 2y³ − 5xy + 3x³

Grocery Shopping and Budgeting

• When shopping for fruits, you might buy different quantities of the same item at different times. For example, if you purchase 3 kg of apples today and 5 kg tomorrow, you simply add the like quantities:
  3 kg apples + 5 kg apples = 8 kg apples.
  
  
• However, you wouldn’t combine apples with oranges: 3 kg apples + 2 kg oranges remains 3 kg apples + 2 kg oranges. This mirrors adding like terms (same items) and leaving unlike terms (different items) separate.

• Like terms: Same letters & powers → add coefficients

• Unlike terms: Different letters or powers → keep separate

• Sign matters: Treat – as part of the number