Summary Basics of Algebra and Factoriation

Algebra
Basics:
- Only variables with the same exponent can added
- When adding like terms, add the coefficients and then places the
variable down
- When multiplying, multiply the coefficients and then the variables. If
the variables are the same, then add the exponents
1) 𝑥 + 𝑥 = 2𝑥 2) 𝑥 × 𝑥 = 𝑥 2
3) 15𝑥 2 + 7𝑥 2 = 22𝑥 2 4) 5𝑥 3 × 3𝑥 = 15𝑥 4
5) 4𝑥 3 + 𝑥 2 = 4𝑥 3 + 𝑥 2 → 6) 3𝑥 × 2𝑦 = 6𝑥𝑦
𝑇ℎ𝑒𝑠𝑒 𝑎𝑟𝑒 𝑢𝑛𝑙𝑖𝑘𝑒 𝑡𝑒𝑟𝑚𝑠
(𝑎+𝑏)
- When a bracket is over a bracket, e.g. (𝒂+𝒃), look if the top
expression’s sign is the same as the bottom expression’s and if all the
variables have the same coefficients. If both of these conditions are
met, then ONLY can we cancel out brackets. Additionally, the
exponential laws come in handy
𝑥+𝑦 (𝑥+𝑦)2
1) =1 2) =𝑥+𝑦
𝑥+𝑦 𝑥+𝑦
(𝑥+𝑦 )4 1 2𝑥 5 1
3)
(𝑥+𝑦 )6
=( 4) =
𝑥+𝑦)2 2𝑥 8 2𝑥 3
Exponential Laws

Rule Expression Examples
Multiplication 𝑎 × 𝑎 𝑦 = 𝑎 𝑥+𝑦
𝑥 (2𝑥 2 )(4𝑥 3 ) = 8𝑥 5
Division 𝑎𝑥 3𝑥 4 𝑥 2
𝑎 ÷ 𝑎 = 𝑦 = 𝑎 𝑥−𝑦
𝑥 𝑦
=
𝑎 6𝑥 2 2
Power of a Products (𝑎 𝑥 )𝑦 = 𝑎 𝑥𝑦 (52 )4 = 58 = 390 625
Power of a Fractions 𝑎 𝑥 𝑎𝑥 2 3 23 8
( ) = 𝑥 ( ) = 3=
𝑏 𝑏 3 3 27
Zero Exponent 0
𝑎 =1 0
4 =1
𝑥0 = 1
(2𝑥)0 = 20 𝑥 0
= (1)(1)
=1