Solve (7x^2+3xy+6y^2)-(-5x^3^+5xy+6{x}^2-{y}^2)-(6{x}^3+4xy-2{y}^2+x2

$$(7 { x }^{ 2 } +3xy+6 { y }^{ 2 } )-(-5 { x }^{ { 3 }^{ } } +5xy+6 { x }^{ 2 } - { y }^{ 2 } )-(6 { x }^{ 3 } +4xy-2 { y }^{ 2 } +x2$$

Evaluate

$$-x^{3}+\left(3y-x\right)^{2}-x_{2}$$

Solution Steps

Calculate 3 to the power of 1 and get 3.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+5xy+6x^{2}-y^{2}\right)-\left(6x^{3}+4xy-2y^{2}+x_{2}\right)$$

To find the opposite of -5x^{3}+5xy+6x^{2}-y^{2}, find the opposite of each term.

$$7x^{2}+3xy+6y^{2}+5x^{3}-5xy-6x^{2}+y^{2}-\left(6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine 3xy and -5xy to get -2xy.

$$7x^{2}-2xy+6y^{2}+5x^{3}-6x^{2}+y^{2}-\left(6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine 7x^{2} and -6x^{2} to get x^{2}.

$$x^{2}-2xy+6y^{2}+5x^{3}+y^{2}-\left(6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine 6y^{2} and y^{2} to get 7y^{2}.

$$x^{2}-2xy+7y^{2}+5x^{3}-\left(6x^{3}+4xy-2y^{2}+x_{2}\right)$$

To find the opposite of 6x^{3}+4xy-2y^{2}+x_{2}, find the opposite of each term.

$$x^{2}-2xy+7y^{2}+5x^{3}-6x^{3}-4xy+2y^{2}-x_{2}$$

Combine 5x^{3} and -6x^{3} to get -x^{3}.

$$x^{2}-2xy+7y^{2}-x^{3}-4xy+2y^{2}-x_{2}$$

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

$$x^{2}-6xy+7y^{2}-x^{3}+2y^{2}-x_{2}$$

Combine 7y^{2} and 2y^{2} to get 9y^{2}.

$$x^{2}-6xy+9y^{2}-x^{3}-x_{2}$$

Differentiate w.r.t. x

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