Question

Phân tích các đa thức sau thành nhân tử:a^4+b^4+c^4+d^4-4abcd

Answer 1

a) Ta có: \(x^{10}+x^5+1\)

\(=x^{10}-x+x^5-x^2+x^2+x+1\)

\(=x\left(x^9-1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)

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

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

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

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

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