Question

Phân tích các đa thức sau thành nhân tử :   a) (x-y)z^3+(z-x)y^3+(y-z)x^3

Answer 1

t chỉ cho kết quả thôi nhá, còn nhóm nhân tử you tự xử nhá !

=(x-y)(z-x)(z-y)(x+y+z)

Answer 2

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

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

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

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

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

Mk ko chắc

Answer 3

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

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

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

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

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

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

\(=\left(x-y\right)\left(y-z\right)\left(x-z\right)\left(x+y+z\right)\)