Solve 5x^{2}+x+y^{2}+8y-2x^2-31x+38y-2x^2+x^3-y^2

$$5 x ^ { 2 } + x + y ^ { 2 } + 8 y - 2 x ^ { 2 } - 31 x + 38 y - 2 x ^ { 2 } + x ^ { 3 } - y ^ { 2 }$$

Evaluate

$$x^{3}+x^{2}-30x+46y$$

Solution Steps

Combine 5x^{2} and -2x^{2} to get 3x^{2}.

$$3x^{2}+x+y^{2}+8y-31x+38y-2x^{2}+x^{3}-y^{2}$$

Combine x and -31x to get -30x.

$$3x^{2}-30x+y^{2}+8y+38y-2x^{2}+x^{3}-y^{2}$$

Combine 8y and 38y to get 46y.

$$3x^{2}-30x+y^{2}+46y-2x^{2}+x^{3}-y^{2}$$

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

$$x^{2}-30x+y^{2}+46y+x^{3}-y^{2}$$

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

$$x^{2}-30x+46y+x^{3}$$

Differentiate w.r.t. x

$$3x^{2}+2x-30$$