Like and Unlike Algebraic Terms: Definition and Examples

January 13, 2025

Definition: Like terms are algebraic terms that have the same variables raised to the same powers, regardless of their coefficients.
Only like terms can be added or subtracted in algebra.
Examples:
- $3x3x$ and $5x5x$ are like terms because they both have the variable $xx$ .
- $7xy7xy$ and $-2xy-2xy$ are like terms because they both have the variables $xx$ and $yy$ with the same powers.
- $4x24x^2$ and $-9\times2-9x^2$ are like terms because they both contain $x2x^2$ .

Definition: Unlike terms are algebraic terms that have different variables or different powers of the same variable.
Unlike terms cannot be combined through addition or subtraction.
Examples:
- $3x3x$ and $4y4y$ are unlike terms because they have different variables ( $xx$ and $yy$ ).
- $2x2x$ and $2x22x^2$ are unlike terms because they involve the same variable $xx$ but with different powers.
- $5xy5xy$ and $7x2y7x^2y$ are unlike terms because the powers of $xx$ are different ( $x1x^1$ vs $x2x^2$ ).

Addition/Subtraction of Terms:
- Like terms can be added or subtracted by combining their coefficients.
  Example: $3x+5x=8x3x + 5x = 8x$ .
- Unlike terms remain separate.
  Example: $3x+4y=3x+4y3x + 4y = 3x + 4y$ (cannot be simplified further).
Multiplication/Division of Terms:
- Unlike terms can be multiplied or divided without requiring them to be “like.”
  Example: $3x⋅4y=12xy3x \cdot 4y = 12xy$ .

Identify whether the following are like or unlike terms:
1. $6a26a^2$ and $-2a2-2a^2$ .
2. $5xy5xy$ and $7x3y7x^3y$ .
3. $8m8m$ and $3n3n$ .
4. $4x34x^3$ and $9x39x^3$ .