杨辉三角的五次方我要死办法算,用梯等式

Question

杨辉三角的五次方
我要死办法算,用梯等式

Answer 1

(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