MENGENAL SIFAT ALJABAR

 

1)  Sifat Aljabar

a)     Faktor Aljabar

Ø  a² + b² = (a + b)² - 2ab    = (a – b)² + 2ab

Ø  a² - b² = (a + b)(a – b)

Ø  a³ - b³ = (a – b)(a² + b² + ab)

Ø  a⁴ - b⁴ = (a² + b²)(a + b)(a – b)

Ø  a²ᵏ - b²ᵏ = (aᵏ + bᵏ)..........(a² + b²)(a + b) (a – b)

Ø  a³ + b³ = (a + b)(a² + b² - ab)

Ø  a²ᵏ⁻¹ + b²ᵏ⁻¹ = (a + b)(a²ᵏ⁻² - a²ᵏ⁻³.b + a²ᵏ⁻⁴.b² - .........  - a.b²ᵏ⁻³ + b²ᵏ⁻²)

Ø  a²ᵏ⁻¹ - b²ᵏ⁻¹ = (a - b)(a²ᵏ⁻² + a²ᵏ⁻³.b + a²ᵏ⁻⁴.b² + .......  + a.b²ᵏ⁻³ + b²ᵏ⁻²)

 

b)    PRODUK Aljabar

Ø  (a + b)² = a² + 2ab + b²

Ø  (a - b)² = a² + b² - 2ab

Ø  (a + b + c)² = a² + b² + c² + 2(ab + ac + bc)

Ø  (a₁ + a₂ + a₃ + ....... + aₙ)² = a₁² + a₂² + a₃² + ..... + aₙ² + 2(a₁a₂ + a₁a₃ + a₁a₄ + ..... + a₁aₙ + a₂a₃ + a₂a₄ + ...... + a₂aₙ + ........ + )

Ø  (a + b)³   = a³ + 3a²b + 3ab² + b³

Ø  (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

Ø  (a – b)³ = a³ - 3a²b + 3ab² - b³

Ø  (a – b)⁴ = a⁴ - 4a³b + 6a²b² - 4ab³ + b⁴

Ø  (a + b)⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵

Ø  (a – b)⁵ = a⁵ - 5a⁴b + 10a³b² - 10a²b³ + 5ab⁴ - b⁵