Special situations in Factoring

Factoring is something we run into all the time in algebra. It is important to know how to do it. Below are the different types of factoring.


Difference of two squares

• a²- b² = (a + b)(a - b)
  • x²- 25 = (x + 5)(x - 5)
    • y²- 49 = (y + 7)(y - 7)
      • z²- 16 = (z + 4)(a - 4)

Trinomial perfect squares

• a² + 2ab + b² = (a + b)(a + b) or (a + b)²
  • a² + 4a+  4= (a+ 2) (a + 2) or(a +2)²
  • a² + 8a + 16  =   (a +4)( a+ 4 )      or (a +4)²
  • a² + 10a+25  = (a + 5 )( a + 5 )or  (a + 5 )²
• ^{a2 - 2ab + b2 = (a - b)(a - b) or (a - b)2}
  • ^{a2 - 14a + 49 (a - 7)  (a - 7)  or (a - 7)2}
  • ^{a2 - 16a+  64=    (a - 8)   (a -8)   or (a - 8 )2}
  • ^{a2 - 18a+  81    = (a - 9)   (a  - 9 )   or (a - 9)2}

Difference of two cubes

• a³ - b³
  • 3 - cube root 'em
  • 2 - square 'em
  • 1 - multiply and change
    • x3-27
    • x3-1
    • 8y3-125

Sum of two cubes

• a³ + b³ 
  • 3 - cube root 'em
  • 2 - square 'em
  • 1 - multiply and change
  • q3+1
  • a3+125
  • h3+64