Year 9: Simplification and expansion of algebraic expressions

What is Simplification?

Simplifying an algebraic expression means writing it in its simplest form. This usually involves combining like terms and removing brackets.

What is Expansion?

Expanding an algebraic expression means multiplying out the terms. For example, 2(x + 3) means multiplying both 'x' and '3' by 2.

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