Factoring Formulas – Product Formulas

Jumat, 20 Maret 2020

Factoring Formulas

Real numbers: a,b, c

Natura number: n

1.  a² – b² = (a + b) (a – b)

2.  a³ – b³ = (a – b) (a² + ab + b²)

3.  a³ + b³ = (a + b) (a² – ab + b²)

4.  a⁴ – b⁴ = (a² – b²) (a² + b²) = (a – b) (a + b) (a² + b²)

5.  a⁵ – b⁵ = (a – b) (a⁴ + a³b + a²b² + ab³ + ab² + b⁴)

6.  a⁵ + b⁵ = (a + b) (a⁴ – a³b + a²b² – ab³ + ab² + b⁴)

7.  If n odd, then

aⁿ + bⁿ = (a + b) (a^{n – 1} – a^{n – 2} b + a^{n – 3} b² – ... – ab^{n – 2}  + b^{n – 1}).

8.  If n is even, then

aⁿ – bⁿ = (a – b) (a^{n – 1} + a^{n – 2} b + a^{n – 3} b² + ... + ab^{n – 2}  + b^{n – 1}).

aⁿ + bⁿ = (a + b) (a^{n – 1} – a^{n – 2} b – a^{n – 3} b² –  ... + ab^{n – 2} – b^{n – 1}).

Product Formulas

Real numbers: a, b, c

Whole numbers: n, k

1.  (a – b)² = a² – 2ab + b

2.  (a + b)² = a² + 2ab + b

3.  (a – b)³ = a³ – 3a²b + 3ab² – b³  

4.  (a + b)³ = a³ + 3a²b + 3ab² + b³  

5.  (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴

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

7.  Binomial Formula

(a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ a^{n – 1} b + ⁿC₂ a^{n – 2} b² + ... + ⁿC_{n – 1} ab^{n – 1} + ⁿC_n bⁿ,

whereare the binomial coefficients.

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

9.  (a + b + c + ... + u + v)² = a² + b² + c² + ... + u² + v² + 2(ab + ac + ... + au + av + bc + ... bu + bv + ... + uv)

Sumber

Labels: Mathematician

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