Types of Factoring

• Difference of two squares
  • a²- b² = (a + b)(a - b)
  • (a-5)(a+5)
  • (x-10)(x-10)
  • (y-18)(y+18)
• Trinomial perfect squares  
•           x² + 6x + 9 = (x + 3)²
  •   x² − 4x + 4 = (x − 2)²
          x² + 10x + 25 = (x + 5)²
• Sum of two cubes
  • a³ + b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change

Example 1: Factor x³ + 125.


Example 2: Factor 8 x³ − 27.


Example 3: Factor 2 x³ + 128 y³.
First find the GFC. GFC = 2

• Sum of two cubes
  • a³ - b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change 
    •  
      x3 − 27= (x − 3)(x2 + 3x+ 9)  
    
    125 − x3=(5 − x)(25 + 5x + x2)
  • 
    1 − a3=(1 − a)(1 + a+ a2)
    
• Binomial expansion
  • (a + b)³ = Use the pattern
  • (a + b)⁴ = Use the pattern
  (5x - y)³ = 125x ³ -75x ² y + 15xy ² - y ³.

  (2x + 3y)4 =16x 4 +96x 3 y + 216x 2 y 2 +216xy 3 +81y 4