Question

Chứng tỏ rằng \(x^8-y^8⋮\left(x-y\right)\) và \(x^8-y^8⋮\left(x+y\right)\)

Answer 1

thêm x;y thuộc z nhé

\(x^8-y^8=\left(x^4\right)^2-\left(y^4\right)^2=\left(x^4-y^4\right)\left(x^4+y^4\right)=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)

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

vì \(x-y⋮x-y;x,y\in Z\Rightarrow\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)⋮x-y\Rightarrow x^8-y^8⋮x-y\)

\(x+y⋮x+y;x,y\in Z\Rightarrow\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)⋮x+y\Rightarrow x^8-y^8⋮x+y\)

Answer 2

Cảm ơn bạn nha! Bài bạn làm đúng rồi nhé!