Algebra and functions notes

Here are a few notes that are useful when working with algebraic expressions and functions.

1. Remember you simplify an expression by collecting like terms
2. You can also simplify expressions by using rules of indices (powers)
   
3. To expand and expression simply multiply each term inside the brackets by the term outside.
4. Factorising expressions is the opposite of expanding expressions
5. You know an expressions is quadratic if it is in the form ax² + bx + c, where a, b, c are constants and a != 0
6. You can write a number exactly using surds
7. The square root of a prime number is a surd.
8. You can manipulate surds using the rules;
   
9. The following are the rules to rationalise surds
   • Fractions in the form 1/√a, multiply the top and bottom by √a
   • Fractions in the form;
     
     …multiply the top and bottom by a-√b
   • Fractions in the form;
     

     
     …multiply the top and bottom by a+√b