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