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

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