Algebraic Identities

Perfect Square Trinomials

• `(a + b)^2 = a^2 + 2ab + b^2`


• `(a - b)^2 = a^2 - 2ab + b^2`

Difference of Squares

• `a^2 - b^2 = (a + b)(a - b)`

Degree 3 Identities

• `(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3`


• `(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3`


• `a^3 - b^3 = (a - b)(a^2 + ab + b^2)`


• `a^3 - 1 = (a - 1)(a^2 + a + 1)`


• `a^3 + b^3 = (a + b)(a^2 - ab + b^2)`


• `a^3 + 1 = (a + 1)(a^2 - a + 1)`


• `a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)`


• `(a + b + c)^3 = a^3 + b^3 + c^3 + 3(a^2b + a^2c + b^2c + ab^2 + ac^2 + bc^2) + 6abc`

Degree 4 Identities

• `(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4`


• `(a - b)^4 = a^4 - 4a^3b + 6a^2b^2 - 4ab^3 + b^4`


• `a^4 + b^4 = (a + b)^2(a - b)^2 - 2a^2b^2`


• `a^4 + 1 = (a + 1)^2(a - 1)^2 - 2a^2`


• `a^4 - b^4 = (a^2 + b^2)(a^2 - b^2)`
  `= (a^2 + b^2)(a + b)(a - b)`
  `= (a + b)(a^3 - a^2b + ab^2 - b^3)`
  `= (a - b)(a^3 + a^2b + ab^2 + b^3)`


• `a^4 - 1 = (a^2 + 1)(a^2 - 1)`
  ` = (a^2 + 1)(a + 1)(a - 1)`
  ` = (a + 1)(a^3 - a^2 + a - 1)`
  ` = (a - 1)(a^3 + a^2 + a + 1)`


• `(a + b + c)^4 = a^4 + b^4 + c^4 + 4a^3b + 4a^3c + 4b^3c + 6a^2b^2 + 6a^2c^2 + 6b^2c^2 + 4ab^3 + 4ac^3 + 4bc^3 + 12ab^2c + 12abc^2 + 12a^2bc`

Voir aussi

Math Calculators