Question

Phân tích đa thức thành nhân tử

(x - y)³ + (y - z)³ + (z - x)³

a²(b - c) + b²(c - a) + c²(a - b)

Giúp mình với

Answer 1

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

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

b: \(=a^2b-a^2c+b^2c-b^2a+c^2\left(a-b\right)\)

\(=ab\left(a-b\right)-c\left(a-b\right)\left(a+b\right)+c^2\left(a-b\right)\)

\(=\left(a-b\right)\left(ab-ca-cb+c^2\right)\)

\(=\left(a-b\right)\left[a\left(b-c\right)-c\left(b-c\right)\right]\)

\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)