Algebra Identities

  • Difference Of Squares :  a² - b² = (a – b)(a + b)

  • Difference Of Cubes  : a³ –  b³ = (a – b)(a² + ab + b²)

  • Sum Of Cubes : a³ +  b³ = (a + b)(a² - ab + b²)

Special Algebra Expansions 

  • Formula For ( a + b )²  and  ( a - b )²
  ( a + b )² = a² + 2 ab + b²  and  ( a - b )² = a² - 2 ab + b² 
  •  Formula For ( a + b )³  and  ( a - b )³
  ( a + b )³ = a³ + 3a²b +3ab²+ b³  and  ( a - b )³ = a³ - 3a²b +3ab²- b³


Roots Of Quadratic Equations 

 

  • Formula : ax² + bx + c = 0
 

Laws of Exponents

  • (am)(an) = am+n
  • (ab)m = ambm
  • (am)n = amn

  • Fractional Exponents
  • a0 = 1
  • (am)/(an) = am-n
  • a-m= 1/(am)

Binomial Theorem


  • (a + b)1 = a + b
  • (a + b)2 = a2 + 2ab + b2
  • (a + b)3 = a3 + 3a2b + 3ab2 + b3
  • (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 ...and so on...


Rules of Zero

  • 0/x = 0 where x is not equal to 0.
  • a0 = 1
  • 0a = 0
  • a*0 = 0
  • a/0 is undefined (you can't do it)