Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• x^2 - 5^2= (x+5)(x-5)
• 3^2 - 4^2= (3+4)(3-4)
• 6^2 - y^2=(6+y)(6-y)

Trinomial perfect squares

• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
• x^2+ 10x + 25=(x+ 5)(x + 5) or (x + 5)²
• 2^2+ 16x + 16=(2+ 4)(2 + 4) or (2 + 4)²
• y^2+ 12y + 36=(y+ 6)(y + 6) or (y + 6)²
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• x^2- 10x + 25=(x- 5)(x - 5) or (x - 5)²
• 2^2- 16x + 16=(2- 4)(2 - 4) or (2 - 4)²
• y^2- 12y + 36=(y- 6)(y - 6) or (y - 6)²
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 8x³ + 27 = (2x)³ + (3)³ = (2x + 3) (4x² - 6x + 9)
      • 
        
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
• Binomial expansion
• (a + b)³ = (a+b)(a+b)(a+b)
• (a + b)⁴ = (a+b)(a+b)(a+b)(a+b)

End Behaviors

Domain - x values
Range - y values

domain → +∞, range → +∞ (means it rises on the right)

domain → -∞, range → -∞ (means it falls on the left)

• domain → -∞, range → +∞ (means it rises on the left)
• domain → +∞, range → -∞ (means it falls on the right)

• domain → +∞, range → -∞ (falls on the right)
• domain → -∞, range → -∞ (falls on the left)

Degree
0- constant
1-linear
2-quadratic
3-cubic
4-quantic
5-quintic

Terms
monomial
binomial
trinomial
quadrinomial
polynomial