Question

HALLAR USANDO EL TRIANGULO DE PASCAL:
1. (X+Y)^3
2. (X+Y)^4
3. (X+Y)^5

Answer 1

Explicación paso a paso:

1)

$(x + y {)}^{3} =(x {)}^{3} +3 (x {)}^{2} (y) +3 (x)(y {)}^{2} + (y {)}^{3} = \\ {x}^{3} + 3 {x}^{2}y + 3x {y}^{2} + {y}^{3}$

2)

$(x + y {)}^{4} = (x {)}^{4 } + 4( x {)}^{3}(y) + 6(x {)}^{2} (y {)}^{2} + 4(x)(y {)}^{3} + (y {)}^{4} = {x}^{4} + 4 {x}^{3} y + 6 {x}^{2} {y}^{2} + 4x {y}^{3} + {y}^{4}$

3)

$(x + y {)}^{5} = (x {)}^{5} + 5(x {)}^{4} (y) + 10(x {)}^{3} (y {)}^{2} + 10(x {)}^{2} (y {)}^{3} + 5(x)(y {)}^{4} + (y {)}^{5}$

$= {x}^{5} + 5 {x}^{4} y + 10 {x}^{3} {y}^{2} + 10 {x}^{2} {y}^{3} + 5x {y}^{4} + {y}^{5}$