Question

phân tích đa thức thành nhân tử :

a, (x+y)²-(x-y)²

b, xy(x+y)+yz(y+z)+xz(x+z)+2xyz

Answer 1

(x+y)²-(x-y)²

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

= 4xy

Answer 2

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

\(=x\left[y\left(x+y\right)+z\left(x+z\right)+2yz\right]+yz\left(y+z\right)\)

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

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

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

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