Solve (2x^{2}-4xy+y^{2})+(-6x^2-9xy-y^2)+(x^2+xy-8y^2)

$$( 2 x ^ { 2 } - 4 x y + y ^ { 2 } ) + ( - 6 x ^ { 2 } - 9 x y - y ^ { 2 } ) + ( x ^ { 2 } + x y - 8 y ^ { 2 } )$$

Evaluate

$$-3x^{2}-12xy-8y^{2}$$

Solution Steps

Combine 2x^{2} and -6x^{2} to get -4x^{2}.

$$-4x^{2}-4xy+y^{2}-9xy-y^{2}+x^{2}+xy-8y^{2}$$

Combine -4xy and -9xy to get -13xy.

$$-4x^{2}-13xy+y^{2}-y^{2}+x^{2}+xy-8y^{2}$$

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

$$-4x^{2}-13xy+x^{2}+xy-8y^{2}$$

Combine -4x^{2} and x^{2} to get -3x^{2}.

$$-3x^{2}-13xy+xy-8y^{2}$$

Combine -13xy and xy to get -12xy.

$$-3x^{2}-12xy-8y^{2}$$

Differentiate w.r.t. x

$$-6x-12y$$