Section Two - Algebra

Basics
1. Negative Numbers
  1. + + makes +
    1. + - makes -
      1. - + makes _
        - - makes +
2. letters multiplied
  1. abc = a x b x c
    1. gn2 = g x n x n
      1. (gn)2 = g x g x n x n
        p(q-r)3 = p x (q-r) x (q-r) x (q-r)
Powers and Roots
1. Rules
  1. When multiplying, you add the powers
    1. When dividing, you subtract the powers
      1. When raising one power to another, you multiply them
        Anything to the power of 1 equals itself
        Anything to the power of 0 is 1
        1 to any power is still 1
        Fractions - Apply the power to the top and bottom
2. Tricky rules
  1. Negative powers - turn it upside down (Reciprocal)
    1. Fractional powers - 1/2 = Square root, 1/3 = Cube root, 1/4 = Fourth root
      1. Two-stage Fractional powers - with powers like 64 5/6, always split the fraction into a root and power,
Brackets
1. Single Brackets
  1. The number outside the brackets multiplies each term inside the bracket
  2. 4a(3b-2c)
    1. 12ab - 8ac
2. Double Brackets
  1. Multiply everything in the first bracket by everything in the second bracket
    1. FOIL method
      1. First - multiply the first term in each bracket together
        Outside - multiply the outside terms
        Inside - multiply the inside terms
        Last - multiply the second term in each bracket together
  2. (2p - 4)(3p + 1) = 6p2 + 2p -12p -4
    1. 6p2 - 10p -4
3. Triple Brackets
  1. Multiply the first two brackets
    1. Then multiply the product by the third bracket

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Section Two - Algebra

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