2:

-8x^6-12x^4y-6x^2y^2-y^3

=-(8x^6+12x^4y+6x^2y^2+y^3)

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

3:

=(1/3)^2-(2x-y)^2

=(1/3-2x+y)(1/3+2x-y)

(x+y+z)(x+z-y)(x+y-z)(y+z-x)

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

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

=(x^2+2xy+y^2-z^2][y^2-x^2-2xz-z^2]

=x^2y^2-x^4-2x^3z-x^2z^2+2xy^3-2x^3y-4x^2yz-2xyz^2+y^4-y^2x^2-2xy^2z-z^2y^2-y^2z^2+x^2z^2+2xz^3+z^4

Ta có:\(2\left(x-y\right)\left(z-y\right)+2\left(y-z\right)\left(z-x\right)+2\left(y-z\right)\left(x-z\right)\)

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

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

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

\(=x^2-2xy+y^2+y^2-2yz+z^2+z^2-2zx+x^2\)

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

a) Ta có:

(x+y+z)(x-y-z) = x^2 -xy -xz +yx- y^2 -yz+zx -zy -z^2

=x^2 - y^2 - 2yz - z^2.

b) Ta có: (x-y+z)(x+y+z) = x^2 +xy+xz -yx-y^2 -yz +zx+zy +z^2

=x^2 +2xz- y^2 +z^2.

c) Ta có: -16 + (x-3)^2 = -16 + ( x^2-6x+9)

= -16 + x^2 - 6x + 9

= x^2 - 6x - 7.

\(a,\left(x+y+z\right)\left(x-y-z\right)\)

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

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

\(=x^2-y^2-2yz-z^2\)

\(b,\left(x-y+z\right)\left(x+y+z\right)\)

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

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

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

\(c,-16+\left(x-3\right)^2\)

\(=-16+x^2-6x+9\)

\(=x^2-6x-7\)

Ta có:\(\left(x-y+z\right)\left(x+y+z\right)=\left[\left(x+z\right)-y\right]\left[\left(x+z\right)+y\right]\)

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

Xong rồi đấy,chúc bạn học tốt

a, (x + y + z)(x - y - z)

= x^2 - xy - xz + xy - y^2 - zy + zx - zy - z^2

= x^2 + y^2 + z^2 + (xy - xy) + (xz - xz) - (zy + zy)

= x^2 + y^2 + z^2 - 2zy

b, (x - y + z)(x + y + z)

= x^2 + xy + xz - xy - y^2 - zy + zx + zy + z^2

= x^2 + y^2 + z^2 + (xy - xy) + xz + xz + (zy - zy)

= x^2 + y^2 + z^2 + 2zx

  ( x + y + z +t )( x + y - z - t)

= ( x + y)^2 - ( z + t)^2 

= x^2 + 2xy + y^2 - z^2 - 2zt - t^2