Solve {l}{4xy-2x^2-2xy+4y^2}{+3x^2-6xy+3y^2}

$$\left. \begin{array} { l } { 4 x y - 2 x ^ { 2 } - 2 x y + 4 y ^ { 2 } } \\ { + 3 x ^ { 2 } - 6 x y + 3 y ^ { 2 } } \end{array} \right.$$

Evaluate

$$x^{2}-4xy+7y^{2}$$

Solution Steps

Combine 4xy and -2xy to get 2xy.

$$2xy-2x^{2}+4y^{2}+3x^{2}-6xy+3y^{2}$$

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

$$2xy+x^{2}+4y^{2}-6xy+3y^{2}$$

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

$$-4xy+x^{2}+4y^{2}+3y^{2}$$

Combine 4y^{2} and 3y^{2} to get 7y^{2}.

$$-4xy+x^{2}+7y^{2}$$

Differentiate w.r.t. x

$$2\left(x-2y\right)$$