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