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Quadratic Expressions (Factoring (ax^2+bx+c (When a=1 (Find d and e. The…

- - - - Can be verified using distributive property
  - - - x+y is the repeated variable, a and b are the two coefficients
  - - - Find d and e. The sum of d and e equals b, the product of d and e equals c
      - Example:
        x+5y+4
        4+1=5, 4(1)=4
        =(x+4)(x+1)
    - - find d and e. the sum of d and e equals b, the product of d and e equals the product of a and c
        
        replace b with d and e using decomposition
        
        Decomposition turns one term into two, both new terms have the same variable
        
        Use group factoring to factor further
        
        Use Binomial Common Factoring to factor further
      - Example:
        8x^2+16x+6
        d+e= 16
        12+4=16
        d(e) = 48
        12(4) = 48
        8x^2+12x+4x+6
        4x(2x+3)+2(2x+3)
        (2x+3)(4x+2)
    - - If c is not a constant, its variable must be factored out
  - - - The first and third term must be perfect squares, and the middle term must be double the product of the first and last terms' coefficients
      - Factored Format: (a+b)^2
      - Example:
        x^2+14+49
        =(x+7)^2
- - - - Shortcut: a^2-2ab+b^2
      - Example:
        (3y-5)^2
        =(3y)^2-2(3y)(5)+(5)^2
        =9y^2-30y+25
    - - Shortcut: a^2+2ab+b^2
      - Example:
        (3y+5)^2
        =(3y)^2+2(3y)(5)+(5)^2 =9y^2+30y+25
  - - - Multiply each term according to foil, then collect like terms
      - Example:
        (4y+3)(2x-2)
        =8yx-8y+6x-6
  - - - simplified to a^2-b^2
        
        Example (3-4)(3+4) =3^2-4^2