Solve (x-1)(y+2)(z-2)+(y-1)(z-2)(x-1)+(z+1)(x+2)(y+1)-(z+1)(y+2)(x-1)-(y-1)(x+2)(z-2)-(x-1)(z-2)(y+1)=

\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.

Apply the distributive property by multiplying each term of x-1 by each term of y+2.

Apply the distributive property by multiplying each term of xy+2x-y-2 by each term of z-2.

Apply the distributive property by multiplying each term of y-1 by each term of z-2.

Apply the distributive property by multiplying each term of yz-2y-z+2 by each term of x-1.

Combine xyz and yzx to get 2xyz.

Combine -yz and -yz to get -2yz.

Combine -2xy and -2yx to get -4xy.

Combine 2y and 2y to get 4y.

Combine 2xz and -zx to get xz.

Combine -2z and z to get -z.

Combine -4x and 2x to get -2x.

Subtract 2 from 4 to get 2.

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.

Solve (x-1)(y+2)(z-2)+(y-1)(z-2)(x-1)+(z+1)(x+2)(y+1)-(z+1)(y+2)(x-1)-(y-1)(x+2)(z-2)-(x-1)(z-2)(y+1)= | Microsoft Math Solver (2024)

FAQs

What is the solution to the equation? ›

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.

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How do you solve the equation? ›

In order to solve equations, you need to work out the value of the unknown variable by adding, subtracting, multiplying or dividing both sides of the equation by the same value. Combine like terms. Simplify the equation by using the opposite operation to both sides. Isolate the variable on one side of the equation.

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What is the solution to the equation 6y 2 y 1 )= 3 y 2 )+ 6? ›

Summary: The solution to the equation 6y - 2(y + 1) = 3(y - 2) + 6 is y = 2.

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How do you solve an X and Y equation? ›

The basic idea is to graph both equations, and find the point where they intersect. The x and y values at this point will give us the value of x and the value of y in the system of equations.

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How do you find the solution to a quadratic equation? ›

The solutions of a quadratic equation ax² + bx + c = 0 are given by the quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula, just get the equation into standard form ax² + bx + c = 0, and apply the quadratic formula.

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What is the golden rule for solving equations? ›

Do unto one side of the equation, what you do to the other! An equation is like a balance scale. If we put something on, or take something off of one side, the scale (or equation) is unbalanced. When solving math equations, we must always keep the 'scale' (or equation) balanced so that both sides are ALWAYS equal.

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How many solutions does Y =- 6x 2 12x 2y =- 4? ›

The linear system of equations y = -6x + 2 and -12x - 2y = -4 has infinitely many solutions.

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What is the solution to the system of equations 2x y 1 3x y =- 6? ›

Summary: The solution to the linear equation 2x+y=1 and 3x-y=-6 is (-1, 3).

How to find x in math? ›

There are a few different ways to solving for x. One method is by using inverse operations. This means that you can use addition and subtraction to solve for x if the equation includes multiplication or division. For example, if you have the equation 4x=12, you can divide both sides by 4 to get x=3.

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What are x and y in math called? ›

These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate. Any point on the coordinate plane can be located or represented using these two axes in the form of an ordered pair of the form (x,y).

How do you know what solution an equation is? ›

If we can solve the equation and get something like x=b where b is a specific number, then we have one solution. If we end up with a statement that's always false, like 3=5, then there's no solution. If we end up with a statement that's always true, like 5=5, then there are infinite solutions..

What is the solution for the equation 5 3b 3 2b 2 5 2 b 3 2? ›

Summary: The solution to the equation 5/(3b³ -2b² - 5) = 2/(b³ - 2) are b = 0 and b = 4.

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What is the solution of 30.16-17.56 5x? ›

Expert-Verified Answer

Thus, the value of x is 2.52.

What is the solution of this equation 7y = 4, 9y = 13, 4y? ›

The solution to the equation 7y - 4 = 9y + 13 - 4y is y = 17/2 or y = 8.5, after simplification and solving for y.

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Solve (x-1)(y+2)(z-2)+(y-1)(z-2)(x-1)+(z+1)(x+2)(y+1)-(z+1)(y+2)(x-1)-(y-1)(x+2)(z-2)-(x-1)(z-2)(y+1)= | Microsoft Math Solver (2024)

FAQs

What is the solution to the equation? ›

How to find x in math? ›

References