\(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

\(=\left(2-z\right)\left(x^2+y^2-1\right)\)

\(2x^2+2y^2-x^2z-y^2z-2=x^2\left(2-z\right)+y^2\left(2-z\right)-\left(2-z\right)=\left(2-z\right)\left(x^2+y^2-1\right)\)

b: \(=\dfrac{12\left(y-z\right)^4+3\left(y-z\right)^5}{6\left(y-z\right)^2}=2\left(y-z\right)^2+\dfrac{1}{2}\left(y-z\right)^3\)

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

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

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

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

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

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

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

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

Mình nghĩ bạn ghi đề sai, đề đúng theo mình là:

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

\(=x^2y^2\left(x-y\right)-y^2z^2\text{[}\left(x-y\right)+\left(z-x\right)\text{]}+z^2x^2\left(z-x\right)\)

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

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

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

\(=\left(x-y\right)\left(x-z\text{ }\right)\text{[}y^2.\left(x+z\right)-z^2\left(x+y\right)\text{]}\)

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

\(=\left(x-y\right)\left(z-x\right)\text{[}\left(y^2x-z^2x\right)+\left(y^2z-z^2y\right)\text{]}\)

\(=\left(x-y\right)\left(z-x\right)\text{[}x.\left(y-z\right)\left(y+z\right)+yz\left(y-z\right)\text{]}\)

\(=\left(x-y\right)\left(x-z\right)\left(y-z\right)\left(xy+x\text{z}+yz\right)\)

tuổi con HN là :

50 : ( 1 + 4 ) = 10 ( tuổi )

tuổi bố HN là :

50 - 10 = 40 ( tuổi )

hiệu của hai bố con ko thay đổi nên hiệu vẫn là 30 tuổi

ta có sơ đồ : bố : |----|----|----|

                  con : |----| hiệu 30 tuổi

tuổi con khi đó là :

 30 : ( 3 - 1 ) = 15 ( tuổi )

số năm mà bố gấp 3 tuổi con là :

 15 - 10 = 5 ( năm )

       ĐS : 5 năm

mình nha

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

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

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

b) \(x^3-x+3x^2y+3xy^2+y^3-y\)

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

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

\(=\left(x+y\right)\left(x^2-xy+y^2+3xy-1\right)\)

\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)