Year 8 Algebra Cheat Sheet
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Year 8 Algebra Cheat Sheet
🔧 Part 1: Expanding Expressions
Key Rule: Distributive Property
a(b + c) = ab + ac
Multiply the term outside the brackets by each term inside the brackets.
3(x + 4) = 3 × x + 3 × 4 = 3x + 12
2x(3x - 5) = 2x × 3x + 2x × (-5) = 6x² - 10x
Expanding and Simplifying
When you have multiple brackets, expand each separately then combine like terms.
= 2x + 6 + 4x - 4 = 6x + 2
🔍 Part 2: Factorising Expressions
Step 1: Find the Highest Common Factor (HCF)
Look for the largest number and highest power of variables that divides into all terms.
Numbers: HCF of 12 and 8 = 4
Variables: HCF of x² and x = x
Therefore, HCF = 4x
Step 2: Factorising by Taking Out Common Factors
Key Rule: ab + ac = a(b + c)
HCF = 3
6x + 9 = 3(2x + 3)
⚡ Part 3: Quick Check - Expanding vs Factorising
Remember: Expanding and factorising are opposite operations!
Expand and simplify: 2(3x + 1) - (x - 4)
Hint: Remember that -(x - 4) = -x + 4
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