\(x^6-y^6\)
\(\Leftrightarrow\left(x^3\right)^2-\left(y^3\right)^2\)
\(\Leftrightarrow\left(x^3-y^3\right)\left(x^3+y^3\right)\)
Vậy .....................................................
\(x^6-y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)\)
\(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)\\ =\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)\)
\(x^6-y^6\)
\(=\left(x-y\right).\left(x^5+x^4y+x^3y^2+x^2y^3+xy^4+y^5\right)\)
Tổng quát:
\(x^n-y^n\)
\(=\left(x-y\right).\left(x^{n-1}+x^{n-2}y+x^{n-3}y^2+...+x^2y^{n-3}+xy^{n-2}+y^{n-1}\right)\)
Chúc bạn học tốt!!!
