Identifying special situations in factoring

• Difference of two squares
• a²- b² = (a + b)(a - b)
• 3 examples
• 3² - 2²= (3+2)(3-2)
• 4² - 1² = (4+1)(4-1)
• 2² - 1²  = (2+1)(2-1)
• Trinomial perfect squares
• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
• 3 examples
• 4x² + (2)(4x)(1) + 1² = (4x+1)²
• 3x² + (2)(3x)(2) + 2² = (3x+2)²
• X² + (2)(X)(8) + 8² = (X+8)²
• a2 - 2ab + b² = (a - b)(a - b) or (a - b)²
• 3 examples
• 6x² - 2(6x)(10) + 10² = (6x-10)²
• 9x² - 2(9x)(5) + 5 = (9x-5)²
• 4x² - 2(4x)(12y) + 12y = (4x-12y)²

Difference of two cubes

• a³ - b³
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• 3 examples
• x³ - 125 = (x-5)(x² + 5x + 25)
• x³ - 64= (x-4)(x²+4x+16)
• x³ - 27= (x-3)(x²+3x+9)

Sum of two cubes

• a³ + b³ 
• 3 - cube root 'em
• 2 - square 'em
• 1 - multiply and change
• 3 examples
• x³ + 8 = (x+2)(x²-2x+ 4)
• x³ + 27= (x+3)(x²-3x +9)
• x³ + 125 = (x+5)(x²-5x +25)

Binomial expansion

• (a + b)³ = Use the pattern a³+3a²b+3ab²+b³
• (a + b)⁴ = Use the pattern a^4+4a³b+6a²b²+4ab³+b^4