Identifying Special Situtations in Factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• x^2-4^2 = (x+4)(x-4)
• p^2-8^2 = (x+8)(x-8)
• 11^2-y^2 = (11+y)(11-y)

Trinomial perfect squares

• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
1. 36+12x+x^2 = (6+x)^2
2. 2x^2+13x+21 = (2x+7)(x+3) 
3. 4x^2+y^2+4xy = (2x+y)^2
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• 16x^2+8xy+y^2 = (4x+y)^2
• y^2-8y+16 = (y-4)^2
• 16x^2+24xy+9y^2 = (4x+3y)^2

Difference of two cubes

• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• s^3-1 = (s-1)(s^2+s+1)
• x^3-27 = (x-3)(x^2+3x+9)
• 8y^3-125

Sum of two cubes

• a³ + b³ 
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change 
•  s^3-1 = (s-1)(s^2+s+1)
• x^3-27 = (x-3)(x^2+3x+9)
• 8y^3-125 = (2y-5)

Binomial expansion

• (a + b)³ = a^3+3a^2b+3ab^2+b^3
• (a + b)⁴ = a^4+4a^3b+6a^2b^2+4ab^3+b^4

End Behaviors

Domain- X-Values (x --> +∞)

Range- Y Values (y --> -∞)

 

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

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

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

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