Question

\(x^8-1\)

phan tich da thuc thanh nhan tu

Answer 1

\(x^8-1=x^8-x^4+x^4-1\)

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

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

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

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

Answer 2

\(x^8-1\)

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

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

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

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