\(z^3\left(x+y^2\right)+y^3\left(z-x^2\right)-x^3\left(y+z^2\right)-xyz\left(xyz-1\right)\)

\(=xz^3+y^2z^3+y^3z-x^2y^3-x^3-x^3z^2-x^2y^2z^2+xyz\)

\(=\left(y^2z^3+y^3z\right)+\left(xz^3+xyz\right)-\left(x^2y^3+x^2y^2z^2\right)-x^3\left(y+z^2\right)\)

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

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

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

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

Tick hộ nha bạn 😘

z^3(x+y^2)+y^3(z-x^2)-x^3(y+z^2)-xyz(xyz-1)

Do câu d mình ko biết làm bởi v mình không làm được

a: =(x-z)(y+8)

b; =x^2-2x-3x+6

=(x-2)(x-3)

c: =x^4+10x^2-x^2-10

=(x^2+10)(x^2-1)

=(x^2+10)(x-1)(x+1)

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

Khai triển ra ta được: 

\(=\left[xyz+\left(xy^2+yx^2\right)+\left(xz^2+zx^2\right)+\left(yz^2+zy^2\right)+xyz\right]+xzy\)

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

\(A=\left(xy+xz+yz\right)\)và \(B=\left(-xy-xz-yz\right)\)

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

\(=xy\left(x+y+1\right)+xz\left(x+z+1\right)+yz\left(y+z+1\right)+xy\left(z-1\right)+xz\left(y-1\right)+yz\left(x-1\right)\)

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

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

`a, 4a^2 + 4a + 1 = (2a+1)^2`

`b, -3x^2 + 6xy - 3y^2`

` = -3(x-y)^2`

`c, (x+y)^2 - 2(x+y)z + z^2`

`= (x+y-z)^2`

\(a,=x\left(x^2-4x+4-z^2\right)=x\left[\left(x-2\right)^2-z^2\right]=x\left(x-z-2\right)\left(x+z-2\right)\\ b,=\left(x-y\right)^2-\left(z-5\right)^2=\left(x-y-z+5\right)\left(x-y+z-5\right)\)

\(x^3-4x^2+4x-xz^2=x\left(x^2-4x+4-z^2\right)\)

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

\(x^2-2xy+y^2-z^2+10z-25\)

\(=\left(x-y\right)^2-\left(z-5\right)^2\)

\(=\left(x-y+z-5\right)\left(x-y-z+5\right)\)

a. x³ - 4x² + 4x - xz²

= x(x² - 4x + 4 ) - z²

= x(x - 4)² - z²

=x( x - 4 - z ) ( x - 4 + z )

b. x² - 2xy +y² - z² + 10z - 25

= ( x - y )² -  ( z - 5 )²

= ( x - y - z + 5 )(x - y + z - 5 )

`@` `\text {Ans}`

`\downarrow`

`a,`

`3x + 6xy + 3y - 3z`

`= 3(x + 2y + y - z)`

`b,`

`x+ xy - xz - xyz`

`= x(1 + y)*(1-z)`

a: 3x^2+6xy+3y^2-3z^2

=3(x^2+2xy+y^2-z^2)

=3[(x+y)^2-z^2]

=3(x+y+z)(x+y-z)

b: x+xy-xz-xyz

=x(y+1)-xz(y+1)

=(y+1)*x*(1-z)

`a, P = 2x(3 - x^2)`

`b, Q = 5x^2(x-3y)`

`c, R = xy(3x^2y^2 - 6y^2z + 1)`

a) \(P=6x-2x^3\)

\(P=2x\left(3+x^2\right)\)

b) \(Q=5x^3-15x^2y\)

\(Q=5x^2\left(x-3y\right)\)

c) \(R=3x^3y^3-6xy^3z+xy\)

\(R=xy\left(3x^2y^2-6y^2z+1\right)\)