Year 8: Simplification and expansion of algebraic expressions

This cheat sheet covers simplification and expansion of algebraic expressions - key skills for year 8!

Simplification

Removing brackets

• Basic distribution:$a(b+c)=ab+ac$
• Negative signs:$-a(b+c)=-ab-ac$

Combining like terms

• Like terms have the same variable raised to the same power. Example: $2x+3x=5x$
• You can only add or subtract coefficients (numbers) of like terms.

Expansion

Multiplying out brackets

• $a(b+c)=ab+ac$ (Same as removing brackets!)
• $(a+b)(c+d)=ac+ad+bc+bd$ (Remember to multiply everything inside the bracket)

Example:$(x+2)(y+3)=xy+3x+2y+6$