\left(xy+2x-y-2\right)\left(z-2\right)+\left(y-1\right)\left(z-2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of y+2.
xyz-2xy+2xz-4x-yz+2y-2z+4+\left(y-1\right)\left(z-2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of xy+2x-y-2 by each term of z-2.
xyz-2xy+2xz-4x-yz+2y-2z+4+\left(yz-2y-z+2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of y-1 by each term of z-2.
xyz-2xy+2xz-4x-yz+2y-2z+4+yzx-yz-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of yz-2y-z+2 by each term of x-1.
2xyz-2xy+2xz-4x-yz+2y-2z+4-yz-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine xyz and yzx to get 2xyz.
2xyz-2xy+2xz-4x-2yz+2y-2z+4-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -yz and -yz to get -2yz.
2xyz-4xy+2xz-4x-2yz+2y-2z+4+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2xy and -2yx to get -4xy.
2xyz-4xy+2xz-4x-2yz+4y-2z+4-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2y and 2y to get 4y.
2xyz-4xy+xz-4x-2yz+4y-2z+4+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xz and -zx to get xz.
2xyz-4xy+xz-4x-2yz+4y-z+4+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2z and z to get -z.
2xyz-4xy+xz-2x-2yz+4y-z+4-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4x and 2x to get -2x.
2xyz-4xy+xz-2x-2yz+4y-z+2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Subtract 2 from 4 to get 2.
2xyz-4xy+xz-2x-2yz+4y-z+2+\left(zx+2z+x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of z+1 by each term of x+2.
2xyz-4xy+xz-2x-2yz+4y-z+2+zxy+zx+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of zx+2z+x+2 by each term of y+1.
3xyz-4xy+xz-2x-2yz+4y-z+2+zx+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xyz and zxy to get 3xyz.
3xyz-4xy+2xz-2x-2yz+4y-z+2+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine xz and zx to get 2xz.
3xyz-4xy+2xz-2x+4y-z+2+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2yz and 2zy to get 0.
3xyz-4xy+2xz-2x+4y+z+2+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -z and 2z to get z.
3xyz-3xy+2xz-2x+4y+z+2+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4xy and xy to get -3xy.
3xyz-3xy+2xz-x+4y+z+2+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2x and x to get -x.
3xyz-3xy+2xz-x+6y+z+2+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 4y and 2y to get 6y.
3xyz-3xy+2xz-x+6y+z+4-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Add 2 and 2 to get 4.
3xyz-3xy+2xz-x+6y+z+4-\left(zy+2z+y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of z+1 by each term of y+2.
3xyz-3xy+2xz-x+6y+z+4-\left(zyx-zy+2zx-2z+yx-y+2x-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of zy+2z+y+2 by each term of x-1.
3xyz-3xy+2xz-x+6y+z+4-zyx-\left(-zy\right)-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
To find the opposite of zyx-zy+2zx-2z+yx-y+2x-2, find the opposite of each term.
2xyz-3xy+2xz-x+6y+z+4-\left(-zy\right)-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 3xyz and -zyx to get 2xyz.
2xyz-3xy+2xz-x+6y+z+4+zy-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -zy is zy.
2xyz-3xy-x+6y+z+4+zy-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xz and -2zx to get 0.
2xyz-3xy-x+6y+z+4+zy+2z-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2z is 2z.
2xyz-3xy-x+6y+3z+4+zy-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine z and 2z to get 3z.
2xyz-4xy-x+6y+3z+4+zy-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -3xy and -yx to get -4xy.
2xyz-4xy-x+6y+3z+4+zy+y-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -y is y.
2xyz-4xy-x+7y+3z+4+zy-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 6y and y to get 7y.
2xyz-4xy-3x+7y+3z+4+zy-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -x and -2x to get -3x.
2xyz-4xy-3x+7y+3z+4+zy+2-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2 is 2.
2xyz-4xy-3x+7y+3z+6+zy-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Add 4 and 2 to get 6.
2xyz-4xy-3x+7y+3z+6+zy-\left(yx+2y-x-2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of y-1 by each term of x+2.
2xyz-4xy-3x+7y+3z+6+zy-\left(yxz-2yx+2yz-4y-xz+2x-2z+4\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of yx+2y-x-2 by each term of z-2.
2xyz-4xy-3x+7y+3z+6+zy-yxz-\left(-2yx\right)-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
To find the opposite of yxz-2yx+2yz-4y-xz+2x-2z+4, find the opposite of each term.
xyz-4xy-3x+7y+3z+6+zy-\left(-2yx\right)-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xyz and -yxz to get xyz.
xyz-4xy-3x+7y+3z+6+zy+2yx-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2yx is 2yx.
xyz-2xy-3x+7y+3z+6+zy-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4xy and 2yx to get -2xy.
xyz-2xy-3x+7y+3z+6-zy-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine zy and -2yz to get -zy.
xyz-2xy-3x+7y+3z+6-zy+4y-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -4y is 4y.
xyz-2xy-3x+11y+3z+6-zy-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 7y and 4y to get 11y.
xyz-2xy-3x+11y+3z+6-zy+xz-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -xz is xz.
xyz-2xy-5x+11y+3z+6-zy+xz-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -3x and -2x to get -5x.
xyz-2xy-5x+11y+3z+6-zy+xz+2z-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2z is 2z.
xyz-2xy-5x+11y+5z+6-zy+xz-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 3z and 2z to get 5z.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Subtract 4 from 6 to get 2.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(xz-2x-z+2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of z-2.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(xzy+xz-2xy-2x-zy-z+2y+2\right)
Apply the distributive property by multiplying each term of xz-2x-z+2 by each term of y+1.
xyz-2xy-5x+11y+5z+2-zy+xz-xzy-xz-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
To find the opposite of xzy+xz-2xy-2x-zy-z+2y+2, find the opposite of each term.
-2xy-5x+11y+5z+2-zy+xz-xz-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine xyz and -xzy to get 0.
-2xy-5x+11y+5z+2-zy-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine xz and -xz to get 0.
-2xy-5x+11y+5z+2-zy+2xy-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
The opposite of -2xy is 2xy.
-5x+11y+5z+2-zy-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine -2xy and 2xy to get 0.
-5x+11y+5z+2-zy+2x-\left(-zy\right)-\left(-z\right)-2y-2
The opposite of -2x is 2x.
-3x+11y+5z+2-zy-\left(-zy\right)-\left(-z\right)-2y-2
Combine -5x and 2x to get -3x.
-3x+11y+5z+2-zy+zy-\left(-z\right)-2y-2
The opposite of -zy is zy.
-3x+11y+5z+2-\left(-z\right)-2y-2
Combine -zy and zy to get 0.
-3x+11y+5z+2+z-2y-2
The opposite of -z is z.
-3x+11y+6z+2-2y-2
Combine 5z and z to get 6z.
-3x+9y+6z+2-2
Combine 11y and -2y to get 9y.
-3x+9y+6z
Subtract 2 from 2 to get 0.
\left(xy+2x-y-2\right)\left(z-2\right)+\left(y-1\right)\left(z-2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of y+2.
xyz-2xy+2xz-4x-yz+2y-2z+4+\left(y-1\right)\left(z-2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of xy+2x-y-2 by each term of z-2.
xyz-2xy+2xz-4x-yz+2y-2z+4+\left(yz-2y-z+2\right)\left(x-1\right)+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of y-1 by each term of z-2.
xyz-2xy+2xz-4x-yz+2y-2z+4+yzx-yz-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of yz-2y-z+2 by each term of x-1.
2xyz-2xy+2xz-4x-yz+2y-2z+4-yz-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine xyz and yzx to get 2xyz.
2xyz-2xy+2xz-4x-2yz+2y-2z+4-2yx+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -yz and -yz to get -2yz.
2xyz-4xy+2xz-4x-2yz+2y-2z+4+2y-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2xy and -2yx to get -4xy.
2xyz-4xy+2xz-4x-2yz+4y-2z+4-zx+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2y and 2y to get 4y.
2xyz-4xy+xz-4x-2yz+4y-2z+4+z+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xz and -zx to get xz.
2xyz-4xy+xz-4x-2yz+4y-z+4+2x-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2z and z to get -z.
2xyz-4xy+xz-2x-2yz+4y-z+4-2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4x and 2x to get -2x.
2xyz-4xy+xz-2x-2yz+4y-z+2+\left(z+1\right)\left(x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Subtract 2 from 4 to get 2.
2xyz-4xy+xz-2x-2yz+4y-z+2+\left(zx+2z+x+2\right)\left(y+1\right)-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of z+1 by each term of x+2.
2xyz-4xy+xz-2x-2yz+4y-z+2+zxy+zx+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of zx+2z+x+2 by each term of y+1.
3xyz-4xy+xz-2x-2yz+4y-z+2+zx+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xyz and zxy to get 3xyz.
3xyz-4xy+2xz-2x-2yz+4y-z+2+2zy+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine xz and zx to get 2xz.
3xyz-4xy+2xz-2x+4y-z+2+2z+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2yz and 2zy to get 0.
3xyz-4xy+2xz-2x+4y+z+2+xy+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -z and 2z to get z.
3xyz-3xy+2xz-2x+4y+z+2+x+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4xy and xy to get -3xy.
3xyz-3xy+2xz-x+4y+z+2+2y+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -2x and x to get -x.
3xyz-3xy+2xz-x+6y+z+2+2-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 4y and 2y to get 6y.
3xyz-3xy+2xz-x+6y+z+4-\left(z+1\right)\left(y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Add 2 and 2 to get 4.
3xyz-3xy+2xz-x+6y+z+4-\left(zy+2z+y+2\right)\left(x-1\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of z+1 by each term of y+2.
3xyz-3xy+2xz-x+6y+z+4-\left(zyx-zy+2zx-2z+yx-y+2x-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of zy+2z+y+2 by each term of x-1.
3xyz-3xy+2xz-x+6y+z+4-zyx-\left(-zy\right)-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
To find the opposite of zyx-zy+2zx-2z+yx-y+2x-2, find the opposite of each term.
2xyz-3xy+2xz-x+6y+z+4-\left(-zy\right)-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 3xyz and -zyx to get 2xyz.
2xyz-3xy+2xz-x+6y+z+4+zy-2zx-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -zy is zy.
2xyz-3xy-x+6y+z+4+zy-\left(-2z\right)-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xz and -2zx to get 0.
2xyz-3xy-x+6y+z+4+zy+2z-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2z is 2z.
2xyz-3xy-x+6y+3z+4+zy-yx-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine z and 2z to get 3z.
2xyz-4xy-x+6y+3z+4+zy-\left(-y\right)-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -3xy and -yx to get -4xy.
2xyz-4xy-x+6y+3z+4+zy+y-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -y is y.
2xyz-4xy-x+7y+3z+4+zy-2x-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 6y and y to get 7y.
2xyz-4xy-3x+7y+3z+4+zy-\left(-2\right)-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -x and -2x to get -3x.
2xyz-4xy-3x+7y+3z+4+zy+2-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2 is 2.
2xyz-4xy-3x+7y+3z+6+zy-\left(y-1\right)\left(x+2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Add 4 and 2 to get 6.
2xyz-4xy-3x+7y+3z+6+zy-\left(yx+2y-x-2\right)\left(z-2\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of y-1 by each term of x+2.
2xyz-4xy-3x+7y+3z+6+zy-\left(yxz-2yx+2yz-4y-xz+2x-2z+4\right)-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of yx+2y-x-2 by each term of z-2.
2xyz-4xy-3x+7y+3z+6+zy-yxz-\left(-2yx\right)-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
To find the opposite of yxz-2yx+2yz-4y-xz+2x-2z+4, find the opposite of each term.
xyz-4xy-3x+7y+3z+6+zy-\left(-2yx\right)-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 2xyz and -yxz to get xyz.
xyz-4xy-3x+7y+3z+6+zy+2yx-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2yx is 2yx.
xyz-2xy-3x+7y+3z+6+zy-2yz-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -4xy and 2yx to get -2xy.
xyz-2xy-3x+7y+3z+6-zy-\left(-4y\right)-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine zy and -2yz to get -zy.
xyz-2xy-3x+7y+3z+6-zy+4y-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -4y is 4y.
xyz-2xy-3x+11y+3z+6-zy-\left(-xz\right)-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 7y and 4y to get 11y.
xyz-2xy-3x+11y+3z+6-zy+xz-2x-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -xz is xz.
xyz-2xy-5x+11y+3z+6-zy+xz-\left(-2z\right)-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine -3x and -2x to get -5x.
xyz-2xy-5x+11y+3z+6-zy+xz+2z-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
The opposite of -2z is 2z.
xyz-2xy-5x+11y+5z+6-zy+xz-4-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Combine 3z and 2z to get 5z.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(x-1\right)\left(z-2\right)\left(y+1\right)
Subtract 4 from 6 to get 2.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(xz-2x-z+2\right)\left(y+1\right)
Apply the distributive property by multiplying each term of x-1 by each term of z-2.
xyz-2xy-5x+11y+5z+2-zy+xz-\left(xzy+xz-2xy-2x-zy-z+2y+2\right)
Apply the distributive property by multiplying each term of xz-2x-z+2 by each term of y+1.
xyz-2xy-5x+11y+5z+2-zy+xz-xzy-xz-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
To find the opposite of xzy+xz-2xy-2x-zy-z+2y+2, find the opposite of each term.
-2xy-5x+11y+5z+2-zy+xz-xz-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine xyz and -xzy to get 0.
-2xy-5x+11y+5z+2-zy-\left(-2xy\right)-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine xz and -xz to get 0.
-2xy-5x+11y+5z+2-zy+2xy-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
The opposite of -2xy is 2xy.
-5x+11y+5z+2-zy-\left(-2x\right)-\left(-zy\right)-\left(-z\right)-2y-2
Combine -2xy and 2xy to get 0.
-5x+11y+5z+2-zy+2x-\left(-zy\right)-\left(-z\right)-2y-2
The opposite of -2x is 2x.
-3x+11y+5z+2-zy-\left(-zy\right)-\left(-z\right)-2y-2
Combine -5x and 2x to get -3x.
-3x+11y+5z+2-zy+zy-\left(-z\right)-2y-2
The opposite of -zy is zy.
-3x+11y+5z+2-\left(-z\right)-2y-2
Combine -zy and zy to get 0.
-3x+11y+5z+2+z-2y-2
The opposite of -z is z.
-3x+11y+6z+2-2y-2
Combine 5z and z to get 6z.
-3x+9y+6z+2-2
Combine 11y and -2y to get 9y.
-3x+9y+6z
Subtract 2 from 2 to get 0.
