Alguien sabe la respuesta de este Monstruo?
(2x+y)^8
Respuestas a la pregunta
Respuesta:
(2x + y)⁸ = 256x⁸ + 1024x⁷y + 1792x⁶y² + 1792x⁵y³ + 1120x⁴y⁴ + 448x³y⁵ + 112x²y⁶ + 16xy⁷ + y⁸
Explicación paso a paso:
El binomio de Newton es la fórmula que nos permite hallar las potencias de un binomio.
(a ± b)ⁿ = (ⁿ ₀)aⁿ ± (ⁿ ₁)aⁿ⁻¹b ± (ⁿ ₂)aⁿ⁻²b² ± ... ±(ⁿ ₙ)bⁿ
(2x+y)⁸
Resolvamos:
(a ± b)ⁿ = (ⁿ ₀)aⁿ ± (ⁿ ₁)aⁿ⁻¹b ± (ⁿ ₂)aⁿ⁻²b² ± ... ±(ⁿ ₙ)bⁿ
(2x + y)⁸ = (⁸₀) (2x)⁸⁻⁰ (y)⁰+(⁸₁) (2x)⁸⁻¹ (y)¹+(⁸₂) (2x)⁸⁻² (y)²+(⁸₃) (2x)⁸⁻³ (y)³+(⁸₄) (2x)⁸⁻⁴ (y)⁴+(⁸₅) (2x)⁸⁻⁵ (y)⁵+(⁸₆) (2x)⁸⁻⁶ (y)⁶+(⁸₇) (2x)⁸⁻⁷ (y)⁷+(⁸₈) (2x)⁸⁻⁸ (y)⁸
(2x + y)⁸ = (1)(2x)⁸ (y)⁰+(8)(2x)⁷ (y)¹+(28)(2x)⁶ (y)²+(56)(2x)⁵ (y)³+(70)(2x)⁴ (y)⁴+(56)(2x)³ (y)⁵+(28)(2x)² (y)⁶+(8)(2x)¹ (y)⁷+(1)(2x)⁰ (y)⁸
(2x + y)⁸ = 256x⁸ + 1024x⁷y + 1792x⁶y² + 1792x⁵y³ + 1120x⁴y⁴ + 448x³y⁵ + 112x²y⁶ + 16xy⁷ + y⁸
Por lo tanto:
(2x + y)⁸ = 256x⁸ + 1024x⁷y + 1792x⁶y² + 1792x⁵y³ + 1120x⁴y⁴ + 448x³y⁵ + 112x²y⁶ + 16xy⁷ + y⁸