根据杨辉三角形公式(a+b)的五次方是多少
2个回答

(a+b)^5

=(a+b)^2*(a+b)^3

=(a^2+2ab+b^2)*(a^3+3a^2b+3ab^2+b^3)

=a^2*(a^3+3a^2b+3ab^2+b^3)

+2ab*(a^3+3a^2b+3ab^2+b^3)

+b^2*(a^3+3a^2b+3ab^2+b^3)

=(a^5+3a^4b+3a^3b^2+a^2b^3)

+(2a^4b+6a^3b^2+6a^2b^3+2ab^4)

+(a^3b^2+3a^2b^3+3ab^4+b^5)

=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5

所以杨辉三角第6行1,5,10,10,5,1