Its Characteristics are: 2 terms, Sum or differnce
and both terms are perfect cubes its formula is
a3 +b3=(a+b)(a2-ab+b2) this is for positive and for negative is
a3 -b3=(a-b)(a2+ab+b2)

Example

1. 8x3 -216 =(2x-6)(4x2+12x+36)
   
   
   

2. 125x3 +64 =(5x+4)(25x2-20x+16)

Factor by grouping (Case #1 and Case #2). In expressions with 4 or 6 terms, we factor two parts of the expression, then the GCF of two terms (each binomial) and then factor the common polynomial factor.

Examples: GCF and CPF

1) 3x3 -6x2 -x+2 = 3x2(x-2)-(x-2)= (x-2)(3x2-1)

2) 4x3-15 +20x2 -3x = 4x3 + 20x2 -3x -15 (rearrange) 4x2(x+5) -3(x+5) = (4x2-3) (x+5)

To factor it we have to separete them in a parenthesis and the common term we divide it for the other terms and separate it with its common.
Its Caractheristics are that one must be divisible for minimum 1 term and it always has 2 terms

Examples

1. 3m2-6mn+4m-8n
   
   

(3m2-6mn)+(4m-8n)
3m(m-2n)+4(m-2n)
=(3m+4)(m-2n)

2. 2x2 -3xy-4x+6y
   
   

(2x2-3xy)- (4x+6y)
x(2x-3y) -2(-2x+3y)
=(2x-3y)(x-2)

Two terms each terms is a perfect square, difference: how to factor: Find the square rrot of both and write them as a product of two binomials with a+ and a-. Note: Sum of square can;t be factored (prime) Note: prime means it can't be factored
Examples:

1) x²-64= (x+8)(x-8)

2) 100x² -9= (10x+3)(10x-3)

Trinomial (written in descending order), coefficient of x² is 1, 2nd term has the most the same letter but with half of the exponent, the 3rd term is a number in most of the cases
Examples:

1.3x+3y=3(x+y)

2.10b-3ab2=b(10-3ab)

Its caracteristics are that the first and the third term has to be perfect In this process of factorization we have to take the square root of the first and the final terms and the result has to be elevated to the square

1. y2+2y +1 = (y+1)2

   
   

2. 8y2+4y+4=

   
   

   (4y+2)2

Trinomial, example: using ac method (grouping) 2d²+15d+18: The product of 2 and 18 is 36 (ac method), you need to find two integers whose product is 36 and whose sum is 15 (12d+3d).

Substitute them for 15d

2d²+12d+3d+18 now are grouping to factor

Examples:

1) 3x² + 10x -8= (x+4)(3x-2)

2) 2x² - 3x -2= (2x+1)(x-2)