Identifying Special Situations In Factoring (:

• Difference of two squares
  • a²- b² = (a + b)(a - b)
    • (2x+1)(2x-1)
    • (3x-2)(3x+2)
    • (x-10)(x+10)
• Trinomial perfect squares
• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
• x²-x+4 = (x-2)²
• x²+6x+9 = (x+3)²
• x²+10x+25 = (x+5)²
• a² + 2ab + b²= (a + b)(a + b) or (a + b)²
• 16x² - 8xy + y² = (4x - y)²
• ^{8xy + y2 + 16x2 = 16x2 + 8xy + y2 = (4x + y)2}
• Difference of two cubes
  • a³ - b³
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • x³-27 = (x-3)(x²+3x+9)
      • s³-1 = (s-1)(s²+s+1)
      • 8y³-125 = (2y-5)(2y²+10y+25)
• Sum of two cubes
  • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • z³+1 = (z+1)(z²+z+1)
      • x³+64 = (x+4)(x²-4x+16)
      • y³+125 = (y+5)(y²-5y+25)
• Binomial expansion
• (a + b)³ = x³ + 3x²y + 3xy² + y³
• (a + b)⁴ = (x+y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴