Solve (4x^{2}-5xy+y^{2})+(-8x^2-8xy-y^2)+(x^2+xy-8y^2)

$$( 4 x ^ { 2 } - 5 x y + y ^ { 2 } ) + ( - 8 x ^ { 2 } - 8 x y - y ^ { 2 } ) + ( x ^ { 2 } + x y - 8 y ^ { 2 } )$$

Evaluate

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

Solution Steps

Combine 4x^{2} and -8x^{2} to get -4x^{2}.

$$-4x^{2}-5xy+y^{2}-8xy-y^{2}+x^{2}+xy-8y^{2}$$

Combine -5xy and -8xy 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

$$-6x-12y$$