Question

phân tích thành nhân tử
\(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)
 

Answer 1

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

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

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

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

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

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

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

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

Answer 2

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

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

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

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

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

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

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