Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• 3 examples
• a² - 9 (a+3) (a-3)
• b² - 4 (b+2) (b-2)
• c² - 1 (c+1) (c-1)

• Trinomial perfect squares
  • a² + 2ab + b² = (a + b)(a + b) or (a + b)²
    • 3 examples
    • a² + 4a + 2 (a+2)²
    • a² + 6a +9 (a+3)²
    • x² + 8x + 16 (x+4)²
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
• 3 examples
• x² - 8x + 16 (x-4)²
• a² - 4a + 2 (a-2)²
• a² - 6a +9 (a-3)²
• Difference of two cubes
• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• 3 examples
• x³-27= (x-3)(x²+3x+9)
• a³-125= (a-5)(a²+5a+25)
• d³-1= (d-1)(d²+d+1)

• Sum of two cubes
• • a³ + b³ 
    • 3 - cube root 'em
    • 2 - square 'em
    • 1 - multiply and change
      • 3 examples
      • x³+27= (x+3)(x²-3x+9)
      • a³+125= (a+5)(a²-5a+25)
      • d³+1= (d+1)(d²-d+1)
• Binomial expansion
  • (a + b)³ = Use the pattern  a³+3a²b+3ab²+b³
  • (a + b)⁴ = Use the pattern  a⁴+4a³b+6a²b²+4ab³+b⁴