Question

Phân tích các đa thức sau thành nhân tử.

a, xy²-9x

b, x²+14x+49-y²

c, xy (x-y)+yz (y-z)+zx (z-x)

Answer 1

a) \(xy^2-9x=x\left(y^2-9\right)=x\left(y+3\right)\left(y-3\right)\)

b) \(x^2+14x+49-y^2=\left(x+7\right)^2-y^2=\left(x+y+7\right)\left(x-y+7\right)\)

c) \(xy\left(x-y\right)+yz\left(y-z\right)+zx\left(z-x\right)\)

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

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

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

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

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