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Factorization, a/=1 - Coggle Diagram

- - - - Characteristics
        
        2 terms
        
        Difference
      - Formula
        
        a^2-b^2=(a+b)(a-b)
      - Examples
        
        x^2-64= (x-8)(x-8)
        
        x^8-16= (x^4+4)(x^4-4)
      - To Factor
        
        Find the root squares of both terms and then organize them.
    - - Characteristics
        
        2 terms
        
        Both terms are perfect cubes
      - Formula
        
        a^3-b^3= (a+b)(a^2+ab+b^2)
        
        a^3+b^3= (a+b)(a^2-ab+b^2)
      - Examples
        
        x^3+8=(x+2)(x^2-2x+4)
        
        1-y^3=(1-y)(1+1y+y^2)
      - To factor
        
        Find the cubic square, then the square root for both terms and multiple the cubic squares
  - - - a=1
        
        Characteristics
        
        2nd term has the same letter but with half of the exponent.
        
        3rd term is a number
        
        a=1
        
        Formula
        
        x2+bx+c
        
        Do rout square of the 1st and find 2 numbers that together multiplied give you the 3rd and added the 2nd
        
        Examples
        
        2x^2-3x+2 2x^2-4x+x-2
        2x(x-2)+(x-2)
        (x-2)(2x+1)
        
        2a^2+5a+3 2a^2+2a+3a+3
        2a(a-1)+3(a-1)
        (a+1)(2a+3)
      - Characteristics
        
        Use ac method
        
        Use method of grouping.
        
        a/=1
    - - Characteristics
        
        1st and 3rd term are perfect squares
        
        1st and 3rd terms are positive
        
        The middle term is twice both squares roots
      - Examples
        
        x^2+12x+36 (x+6)^2
        
        9r^2+48rt+64t (3r+8t)^2
      - Formula
        
        a2+2ab+b2=(a+b)2
        
        a2-2ab+b2=(a-b)2
  - - - Common Monomial Factor
        
        To factor
        
        in expressions with 4 or 6 terms, we factor 2 parts of the expression, polynomial factor.
        
        Characteristics
        
        4-6 terms
        
        they have to be equal so they can be factorized
        
        Examples
        
        x2-16=(x-4) (x+4)
        x2 - 36= (x-6) (x+6)
      - Common Polynomial Factor
        
        characteristics
        
        4-6 terms
        
        They have to have something in common
        
        To factor
        
        the GCF of two or more molinomials is the product of all their common prime factors.
        
        Examples
        
        a(x2-3)-2(x2-3)=
        (x2-3) (a-2)
        
        12a3-9a2+4a-3=
        3a2(4a-3)+(4a-3)= (4a-3)(3a2+1)