Question

phân tích đa thức thành nhân tử: m⁶-m⁴+2m³+2m²

Answer 1

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

\(=\left(m^3-m\right)^2+\left(m^2+m\right)^2\)

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

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

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

Answer 2

\(m^6-m^4+2m^3+2m^2\)

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

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

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