Factorising Made Simple for Year 12
Master the fundamentals of algebraic factorisation Build confidence with step-by-step techniques Apply skills to solve complex equations
What is Factorising?
Breaking down expressions into simpler parts Finding factors that multiply to give the original expression Reverse process of expanding brackets Essential skill for solving equations
Common Factor Method
Look for the highest common factor (HCF) Factor out the common term Example: 6x + 9 = 3(2x + 3) Always check your answer by expanding
Practice: Common Factors
Factor these expressions: a) 4x + 8 b) 15y - 10 c) 6a² + 9a d) 12x³ - 8x²
Difference of Two Squares
Pattern: a² - b² = (a + b)(a - b) Recognise perfect squares Example: x² - 16 = (x + 4)(x - 4) Works with any two squared terms
Quick Check
Which of these can be factored using difference of two squares? A) x² + 25 B) 9y² - 16 C) 4a² - 12 D) 25m² - 49n²
Quadratic Trinomials
Form: ax² + bx + c Find two numbers that multiply to ac and add to b Split the middle term Factor by grouping
Factoring Methods Comparison
{"left":"Common Factor: Look for shared terms first\nDifference of Squares: a² - b² pattern\nTrinomials: Find factor pairs systematically","right":"Perfect Square Trinomials: a² ± 2ab + b²\nGrouping: Factor pairs of terms\nSum/Difference of Cubes: Special patterns"}
Mixed Practice Challenge
Factor completely: 1) 2x² - 8 2) x² + 7x + 12 3) 3x² - 12x + 9 4) 4y² - 25z² 5) x³ + 2x² + x
Key Takeaways
"Factorising is like finding the DNA of an algebraic expression - it reveals the fundamental building blocks that create the whole."