Respuestas
Explicación paso a paso:
Desarrolla las siguientes potencias de binomios utilizando el triángulo de pascal
1.
(4x + 1)⁴ = (⁴₀) (4x)⁴⁻⁰ (1)⁰+(⁴₁) (4x)⁴⁻¹ (1)¹+(⁴₂) (4x)⁴⁻² (1)²+(⁴₃) (4x)⁴⁻³ (1)³+(⁴₄) (4x)⁴⁻⁴ (1)⁴
(4x + 1)⁴ = (1) (4x)⁴ (1)⁰+(4) (4x)³ (1)¹+(6) (4x)² (1)²+(4) (4x)¹ (1)³+(1) (4x)⁰ (1)⁴
(4x + 1)⁴ = 256x⁴ + 256x³ + 96x² + 16x + 1
2.
(3x - 2y)³ = (³₀) (3x)³⁻⁰ (2y)⁰-(³₁) (3x)³⁻¹ (2y)¹+(³₂) (3x)³⁻² (2y)²-(³₃) (3x)³⁻³ (2y)³
(3x - 2y)³ = (1) (3x)³ (2y)⁰-(3) (3x)² (2y)¹+(3) (3x)¹ (2y)²-(1) (3x)⁰ (2y)³
(3x - 2y)³ = 27x³ - 54x²y + 36xy² - 8y³
3.
(3x + 4)⁶ = (⁶₀) (3x)⁶⁻⁰ (4)⁰+(⁶₁) (3x)⁶⁻¹ (4)¹+(⁶₂) (3x)⁶⁻² (4)²+(⁶₃) (3x)⁶⁻³ (4)³+(⁶₄) (3x)⁶⁻⁴ (4)⁴+(⁶₅) (3x)⁶⁻⁵ (4)⁵+(⁶₆) (3x)⁶⁻⁶ (4)⁶
(3x + 4)⁶ = (1) (3x)⁶ (4)⁰+(6) (3x)⁵ (4)¹+(15) (3x)⁴ (4)²+(20) (3x)³ (4)³+(15) (3x)² (4)⁴+(6) (3x)¹ (4)⁵+(1) (3x)⁰ (4)⁶
(3x + 4)⁶ = 729x⁶ + 5832x⁵ + 19440x⁴ + 34560x³ + 34560x² + 18432x + 4096