Question

Phân tích thành nhân tử:   a) x^​2 - x - y^​2 - y                     b) a^​3 - a^​2x - ay + xy                   c) xy (x+y) + yz (y+z) +xz ( x+z) + 3xyz

Answer 1

a) \(x^2-x-y^2-y\)

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

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

\(=\left(x+y\right)\left(x-y-1\right)\)

b) \(a^3-a^2x-ay+xy\)

\(=\left(a^3-ay\right)-\left(a^2x-xy\right)\)

\(=a.\left(a^2-y\right)-x\left(a^2-y\right)\)

\(=\left(a-x\right)\left(a^2-y\right)\)

c) \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+3xyz\)

\(=\left[xy\left(x+y\right)+xyz\right]+\left[yz\left(y+z\right)+xyz\right]+\left[xz\left(x+z\right)+xyz\right]\)

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

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