Question

[Dũng Lương Trí]

Phân tích đa thức thành nhân tử :

a) x²(y-z) + y²(z-x) + z²(x-y)

b) (a+b)³ + (c-a)³ - (a+c)³

c) a³(c-b) + b³(a-c) + c³(b-a)

Answer 1

[Tuấn Nguyễn]

a) \(x^2\left(y-z\right)+y^2\left(z-x\right)+z^2\left(x-y\right)\)

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

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

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

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

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

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

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