Question

Phân tích đa thức thành nhân tử 

\(\left(x^2-2x+2\right)^4-20x^2\left(x^2-2x+2\right)^2+64x^4\)

Answer 1

Khó quá , bó tay 

Answer 2

\(\left(x^2-2x+2\right)^4-20x^2\left(x^2-2x+2\right)+64x^4\)

\(=\left[\left(x^2-2x+2\right)^2\right]^2-2.\left(x^2-2x+2\right)^2.10x^2+\left(10x^2\right)^2-36x^4\)

\(=\left[\left(x^2-2x+2\right)^2-10x^2\right]^2-\left(6x^2\right)^2\)\(=\left[\left(x^2-2x+2\right)^2-4x^2\right]\left[\left(x^2-2x+2\right)^2-16x^2\right]\)

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

\(=\left(x^2+2\right)\left(x^2-4x+2\right)\left(x^2-6x+2\right)\left(x^2+2x+2\right)\)