Year 8: Simplification and expansion of algebraic expressions

This cheat sheet will help you simplify and expand algebraic expressions. Remember to follow the order of operations (BODMAS/PEMDAS).

Simplifying expressions

Like terms

Like terms are terms that have the same variables raised to the same powers. You can combine them to simplify an expression.

• Example: $3x+2x=5x$
• Example: $2y^2+5y^2=7y^2$

Removing brackets (expanding) - the distributive property

When multiplying a number or variable by a bracket, distribute it to all the terms inside the bracket.

• Example: $2(x+3)=2x+6$
• Example: $3(2y-1)=6y-3$

Expanding expressions

Expanding means multiplying out a bracket to get rid of it.

• Example: $(x+1)(x+2)=x^2+2x+x+2=x^2+3x+2$

Key reminders:

• Always simplify before applying any rules.
• Double-check your work!