Expanding and Factorising Quadratics
Think of expanding brackets like unpacking a suitcase - you're taking everything out and spreading it around. When you see something like 4, multiply the 4 by everything inside those brackets to get 4a + 24.
Factorising works the opposite way - you're packing things back into the suitcase by finding the Highest Common Factor (HCF). For example, 4x + 12 becomes 4 because 4 divides into both terms perfectly.
The real fun starts with double brackets like x-5$$x+2. You need to multiply everything in the first bracket by everything in the second bracket - think of it as making sure everyone at two different tables meets everyone at the other table. This gives you x² - 3x - 10 after collecting like terms.
Top Tip: Always check your factorising by expanding the brackets back out - if you get your original expression, you've nailed it!
Squared brackets like ² are just the same bracket multiplied by itself twice. The difference of two squares pattern has a special shortcut: it always factors as x+4$$x-4.
