Question

Phân tích thành nhân tử:

a) x⁶ + 1

b) x⁶ - y⁶

c) x⁹ + 1

Ai làm đúng + có lời giải + nhanh nhất mk tk

Answer 1

a) \(x^6+1=x^6-\left(-1\right)=\left(x^3\right)^2-\left(-1^3\right)^2=\left(x^3\right)^2-\left(-1\right)\)

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

b) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3+y^3\right)\left(x^3-y^3\right)\)

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

\(=\left(x^3+1\right)\left(\left(x^3\right)^2-x^3.1+1^2\right)=\left(x^3+1\right)\left(x^6-x^3+1\right)\)

Answer 2

a)  \(x^6+1=\left(x^6-x^4+x^2\right)+\left(x^4-x^2+1\right)\)

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

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

b)  \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2=\left(x^3-y^3\right)\left(x^3+y^3\right)\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)

c) \(x^9+1=\left(x^9-x^6+x^3\right)+\left(x^6-x^3+1\right)\)

\(=x^3\left(x^6-x^3+1\right)+\left(x^6-x^3+1\right)\)

\(=\left(x^3+1\right)\left(x^6-x^3+1\right)\)

\(=\left(x+1\right)\left(x^2-x+1\right)\left(x^6-x^3+1\right)\)