Solve (x^{2}-y^{2}+1-x^2-y^2)-(1+x^2+y^2)

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

Evaluate

$$-x^{2}-3y^{2}$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

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

Combine -y^{2} and -y^{2} to get -2y^{2}.

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

To find the opposite of 1+x^{2}+y^{2}, find the opposite of each term.

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

Subtract 1 from 1 to get 0.

$$-2y^{2}-x^{2}-y^{2}$$

Combine -2y^{2} and -y^{2} to get -3y^{2}.

$$-3y^{2}-x^{2}$$

Expand

$$-x^{2}-3y^{2}$$

Solution Steps

Combine x^{2} and -x^{2} to get 0.

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

Combine -y^{2} and -y^{2} to get -2y^{2}.

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

To find the opposite of 1+x^{2}+y^{2}, find the opposite of each term.

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

Subtract 1 from 1 to get 0.

$$-2y^{2}-x^{2}-y^{2}$$

Combine -2y^{2} and -y^{2} to get -3y^{2}.

$$-3y^{2}-x^{2}$$