Question

Phân tích đa thức thành nhân tử:

(x-1)⁴ - 2(x² -2x +1)²+1

Answer 1

\(\left(x-1\right)^4-2\left(x^2-2x+1\right)^2+1\)

\(=\left[\left(x-1\right)^2\right]^2-2\left(x-1\right)^2+1^2\)

\(=\left[\left(x-1\right)^2-1\right]^2\)

Answer 2

\(\left(x-1\right)^4-2\left(x^2-2x+1\right)+1=\left[\left(x-1\right)^2\right]^2-2\left(x-1\right)^2+1^2\)

\(=\left[\left(x-1\right)^2-1\right]^2=\left[\left(x-1+1\right)\left(x-1-1\right)\right]^2\)

\(=\left[x\left(x-2\right)\right]^2\)