Question

a^6 - a^4 + 2a^3 + 2a^2

Answer 1

Ta có: \(a^6-a^4+2a^3+2a^2\)

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

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

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

\(=\left(a+1\right)\left(a^5-a^4+2a^2\right)\)

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

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

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

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