Factors and Products Formulas

  1. {(a + b)^2} = {a^2} + 2ab + {b^2}
  2. {(a - b)^2} = {a^2} - 2ab + {b^2}
  3. {(a + b)^2} = {(a - b)^2} + 4ab
  4. {(a - b)^2} = {(a + b)^2} - 4ab
  5. {(a + b)^2} + {(a - b)^2} = 2{a^2} + 2{b^2}
  6. {(a + b + c)^2} = {a^2} + {b^2} + {c^2} + 2ab       + 2bc + 2ac
  7. {(a + b + c +      \cdots )^2} = {a^2} + {b^2} + {c^2} + \cdots     + 2(ab + ac + bc + \cdots )
  8. {(a + b)^3} = {a^3} + 3{a^2}b + 3a{b^2} +       {b^3} = {a^3} + {b^3} + 3ab(a + b)
  9. {(a - b)^3} = {a^3} - 3{a^2}b + 3a{b^2} -       {b^3} = {a^3} - {b^3} - 3ab(a - b)
  10. (a + b)(a - b) = {a^2} - {b^2}
  11. {a^3} - {b^3} = (a - b)({a^2} + ab + {b^2})
  12. {a^3} + {b^3} = (a + b)({a^2} - ab + {b^2})
  13. (a + b)(a + c) = {a^2} + (b + c)a + bc
  14. (x + b)(x + c) = {x^2} + (b + c)x + bc
  15. (a + b + c)({a^2} + {b^2} + {c^2} - ac - bc -       ca) = {a^3} + {b^3} + {c^3} - 3abc
  16. {a^n} - {b^n} = (a - b)({a^{n - 1}} + {a^{n -       2}}b + {a^{n - 3}}{b^2} +       \cdots + {b^{n - 1}}) if n is odd.
  17. {a^n} - {b^n} = (a + b)({a^{n - 1}} - {a^{n -       2}}b + {a^{n - 3}}{b^2} -   \cdots - {b^{n - 1}}) if n is even.
  18. {a^n} + {b^n} = (a + b)({a^{n - 1}} - {a^{n -       2}}b + {a^{n - 3}}{b^2} -      \cdots - {b^{n - 1}}) if n is odd.
  19. (x + a)(x + b)(x + c) = {x^3} + (a + b +       c){x^2} + (ab + bc + ac)x + abc