Solve -2(x-y+z^2)+4(z^2+y-x)+(1-x-y)

$$- 2 ( x - y + z ^ { 2 } ) + 4 ( z ^ { 2 } + y - x ) + ( 1 - x - y )$$

Evaluate

$$1+2z^{2}+5y-7x$$

Solution Steps

Use the distributive property to multiply -2 by x-y+z^{2}.

$$-2x+2y-2z^{2}+4\left(z^{2}+y-x\right)+1-x-y$$

Use the distributive property to multiply 4 by z^{2}+y-x.

$$-2x+2y-2z^{2}+4z^{2}+4y-4x+1-x-y$$

Combine -2z^{2} and 4z^{2} to get 2z^{2}.

$$-2x+2y+2z^{2}+4y-4x+1-x-y$$

Combine 2y and 4y to get 6y.

$$-2x+6y+2z^{2}-4x+1-x-y$$

Combine -2x and -4x to get -6x.

$$-6x+6y+2z^{2}+1-x-y$$

Combine -6x and -x to get -7x.

$$-7x+6y+2z^{2}+1-y$$

Combine 6y and -y to get 5y.

$$-7x+5y+2z^{2}+1$$

Expand

$$1+2z^{2}+5y-7x$$

Solution Steps

Use the distributive property to multiply -2 by x-y+z^{2}.

$$-2x+2y-2z^{2}+4\left(z^{2}+y-x\right)+1-x-y$$

Use the distributive property to multiply 4 by z^{2}+y-x.

$$-2x+2y-2z^{2}+4z^{2}+4y-4x+1-x-y$$

Combine -2z^{2} and 4z^{2} to get 2z^{2}.

$$-2x+2y+2z^{2}+4y-4x+1-x-y$$

Combine 2y and 4y to get 6y.

$$-2x+6y+2z^{2}-4x+1-x-y$$

Combine -2x and -4x to get -6x.

$$-6x+6y+2z^{2}+1-x-y$$

Combine -6x and -x to get -7x.

$$-7x+6y+2z^{2}+1-y$$

Combine 6y and -y to get 5y.

$$-7x+5y+2z^{2}+1$$