Hãy khai triển: a) (x – y)^6; b) (1 + x)^7.

Hướng dẫn giải

a) ${(x – y)}^6$

$=C_6^0{x}^6+C_6^1{x}^5(-y)+C_6^2{x}^4{(-y)}^2+C_6^3{x}^3{(-y)}^3$

$+C_6^4{x}^2{(-y)}^4+C_6^{5}x{(-y)}^5+C_6^6{(-y)}^6$

$=x^6-C_6^1{x}^{5}y+C_6^2{x}^4{y}^2-C_6^3{x}^3{y}^3+C_6^4{x}^2{y}^4-C_6^{5}x{y}^5+y^6$

$=x^6-6x^{5}y+15x^4{y}^2-20x^3{y}^3+15x^2{y}^4-6x{y}^5+y^6.$

b)${(1 + x)}^7$

$=C_7^0{1}^7+C_7^1{1}^{6}x+C_7^2{1}^5{x}^2+C_7^3{1}^4{x}^3$

$+C_7^4{1}^3{x}^4+C_7^5{1}^2{x}^5+C_7^{6}1x^6+C_7^7{x}^7$

= 1 + 7x + 21x2 + 35x3 + 35x4 + 21x5 + 7x6 + x7.