Question

Phân tích đa thức thành nhân tử

\(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

Answer 1

\(\left(x-y\right)^3+\left(y-z\right)^3+\left(z-x\right)^3\)

\(=\left(x-y=y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^3\)\(=\left(x-z\right)\left[x^2-2xy+y^2-\left(xy-xz-y^2+yz\right)+y^2-2yz+z^2\right]-\left(x-z\right)^3\)\(=\left(x-z\right)\left(x^2+z^2-3xy-3yz+xz+3y^2\right)-\left(x-z\right)^3\)

\(=\left(x-z\right)\left[\left(x^2+z^2-3xy-3yz+xz+3y^2\right)-\left(x-z\right)^2\right]\)

\(=\left(x-z\right)\left(3y^2-3xy+3xz-3yz\right)\)

\(=3\left(y^2-xy+xz-yz\right)\left(x-z\right)\)

Answer 2

Nguyễn NamRibi Nkok NgokTrần Quốc LộcPhạm Hoàng GiangAnh TriêtNguyễn Thanh HằngThien Tu Borum

Trương Hồng HạnhNguyễn Huy TúAkai HarumaVõ Đông Anh TuấnPhương AnĐoàn Đức HiếuNguyễn Phương Trâm