Year 8: Simplification and expansion of algebraic expressions

Simplification

Simplifying means making an expression easier to understand. You do this by removing unnecessary terms and combining like terms.

Combining Like Terms

• Like Terms: Terms with the same variables and powers of those variables (e.g., 3x + 2x = 5x).
• To combine like terms, add or subtract their coefficients (the numbers in front of the variables).
• Example: 2x + 3x - x = (2 + 3 - 1)x = 4x

Expansion (or 'Multiplying Out')

Expansion means multiplying out an expression that's been written in brackets. You use the distributive property.

The Distributive Property

• a(b + c) = ab + ac
• Example 1: 2(x + 3) = 2*x + 2*3 = 2x + 6
• Example 2: 3(2x - 1) = 3*2x - 3*1 = 6x - 3

Remember to always multiply everything inside the brackets by the number outside.

Practice makes perfect: Try simplifying and expanding different expressions.