Question

将多项式f（x）＝X∧4－2X∧3＋1展开成关于X－1的多项式.

Answer 1

x^4 = (x - 1 + 1)^4 = (x-1)^4 + 4*(x-1)^3 + 6*(x-1)^2 + 4*(x-1) + 1

x^3 = (x - 1 + 1)^3 = (x-1)^3 + 3*(x-1)^2 + 3*(x-1) + 1

代入f(x)

有

f(x) = (x-1)^4 + 2*(x-1)^3 - 2(x-1)