In algebra, we often work with expressions that contain more than one term.
Simplifying such expressions makes them easier to understand and solve.
To simplify means to make shorter or more compact without changing the value.

Key Concepts

Like Terms

Terms that have the same variable(s) raised to the same power.

 Examples:

• ( 3x ) and ( 7x ) are like terms (both contain ( x ))
• ( 5y^2 ) and ( -2y^2 ) are like terms (both contain ( y^2 ))
• ( 4x ) and ( 5y ) are not like terms (different variables)

2️⃣ Combining Like Terms

Add or subtract the coefficients of like terms while keeping the variable unchanged.

Example 1:
( 3x + 5x = (3 + 5)x = 8x )

Example 2:
( 7a - 4a = 3a )

Example 3:
( 4m + 3n + 5m - 2n = (4m + 5m) + (3n - 2n) = 9m + n )

3️⃣ Simplifying Expressions with Brackets

To simplify expressions with brackets, apply the distributive property:
( a(b + c) = ab + ac )

Example 1:
Simplify ( 2(x + 3) = 2x + 6 )

Example 2:
Simplify ( 5(2a + 3b) - 2(a + b) ) ( = (10a + 15b) - (2a + 2b) = 8a + 13b )

Example 3:
Simplify ( 4(3x - 2) - 3(2x - 1) ) ( = (12x - 8) - (6x - 3) = 6x - 5 )

⚠️ Common Mistakes

• Adding unlike terms (e.g. ( 3x + 2y ) cannot be simplified)
• Forgetting to multiply every term inside a bracket
• Ignoring negative signs before brackets.