Question

Phân tích thành nhân tử: \(\left(x^2-x+2\right)^2+\left(x-2\right)^2\)

Answer 1

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

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

\(=x^4-x^3+2x^2-x^3+x^2-2x+2x^2-2x+4+x^2+4-4x\)

\(=x^4-2x^3+6x^2-6x\)

\(=x\left(x^3-2x^2+6x-6\right)\)

Answer 2

Sai rồi nhé +4+4=8 mà

Answer 3

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

\(=x^4+x^2+4-2x^3-4x+4x^2+x^2-4x+4\)

\(=x^4-2x^3+6x^2-8x+8\)

\(=x^4+4x^2-2x^3-8x+2x^2+8\)

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

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

Answer 4

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

\(=x^4+x^2+4+4x^2-4x-2x^3+x^2-4x+2\)

\(=x^4-2x^3+6x^2-8x+6\)

\(=x\left(x^3-2x^2+6x-2\right)\)