Question

Phân tích thành nhân tử

3(x^4+x^2+1)-(x^2+x+1)^2

Answer 1

\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)

\(=3\left(x^4+x^2+1\right)-\left(x^4+x^2+1\right)\)

\(=\left(x^4+x^2+1\right)\left(3-1\right)\)

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

Answer 2

\(=3\left(x^4+2x^2+1-x^2\right)-\left(x^2+x+1\right)^2\)

\(=3\left(x^2+1-x\right)\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)

\(=\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\)

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

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