Master Expanding Brackets

Expanding Brackets

Ever wondered why we need to expand brackets? It's like unpacking a suitcase - we need to see what's inside! Expanding brackets means multiplying everything inside the brackets by the term outside.

For simple cases like 5$3c + 2$, you multiply 5 by each term inside: 5 × 3c = 15c and 5 × 2 = 10, giving you 15c + 10. When you see letters multiplied together like x$x + 7$, remember that x × x = x², so you get x² + 7x.

Things get more interesting with double brackets like n + 5$$n + 6. Here's where the FOIL method helps: multiply the First terms $n × n = n²$, the Outer terms $n × 6 = 6n$, the Inner terms $5 × n = 5n$, and the Last terms $5 × 6 = 30$. Then combine like terms: n² + 6n + 5n + 30 = n² + 11n + 30.

Top Tip: Always check your work by substituting a simple number for the variable - both the original and expanded forms should give the same answer!