Year 9: Simplification and expansion of algebraic expressions

Rules for simplification

• Like terms: Terms with the same variables and powers added or subtracted together. Example: 3x + 2x = 5x
• Distribute: When multiplying a number outside a bracket by terms inside the bracket. Example: 2(x + 3) = 2x + 6
• Remove brackets: Use the distributive property.

Rules for expansion

• The Product Rule: a(b + c) = ab + ac
• Multiplying Variables: Multiply all variables together.

Examples

Example 1 (Simplification): 3x + 4y + 2x - y = (3x + 2x) + (4y - y) = 5x + 3y

Example 2 (Expansion): 2(x + 3) = 2x + 6

Example 3 (Expansion): 3(2x + 4y) = 6x + 12y