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

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

Evaluate

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

Solution Steps

Combine 6x^{2} and 7x^{2} to get 13x^{2}.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+5xy+13x^{2}-y^{2}+3xy+6y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine 5xy and 3xy to get 8xy.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+8xy+13x^{2}-y^{2}+6y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine -y^{2} and 6y^{2} to get 5y^{2}.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+8xy+13x^{2}+5y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

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

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+8xy+13x^{2}+5y^{2}+4xy-2y^{2}+x_{2}\right)$$

Combine 8xy and 4xy to get 12xy.

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+12xy+13x^{2}+5y^{2}-2y^{2}+x_{2}\right)$$

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

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+12xy+13x^{2}+3y^{2}+x_{2}\right)$$

To find the opposite of x^{3}+12xy+13x^{2}+3y^{2}+x_{2}, find the opposite of each term.

$$7x^{2}+3xy+6y^{2}-x^{3}-12xy-13x^{2}-3y^{2}-x_{2}$$

Combine 3xy and -12xy to get -9xy.

$$7x^{2}-9xy+6y^{2}-x^{3}-13x^{2}-3y^{2}-x_{2}$$

Combine 7x^{2} and -13x^{2} to get -6x^{2}.

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

Combine 6y^{2} and -3y^{2} to get 3y^{2}.

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

Expand

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

Solution Steps

Combine 6x^{2} and 7x^{2} to get 13x^{2}.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+5xy+13x^{2}-y^{2}+3xy+6y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine 5xy and 3xy to get 8xy.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+8xy+13x^{2}-y^{2}+6y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

Combine -y^{2} and 6y^{2} to get 5y^{2}.

$$7x^{2}+3xy+6y^{2}-\left(-5x^{3}+8xy+13x^{2}+5y^{2}+6x^{3}+4xy-2y^{2}+x_{2}\right)$$

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

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+8xy+13x^{2}+5y^{2}+4xy-2y^{2}+x_{2}\right)$$

Combine 8xy and 4xy to get 12xy.

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+12xy+13x^{2}+5y^{2}-2y^{2}+x_{2}\right)$$

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

$$7x^{2}+3xy+6y^{2}-\left(x^{3}+12xy+13x^{2}+3y^{2}+x_{2}\right)$$

To find the opposite of x^{3}+12xy+13x^{2}+3y^{2}+x_{2}, find the opposite of each term.

$$7x^{2}+3xy+6y^{2}-x^{3}-12xy-13x^{2}-3y^{2}-x_{2}$$

Combine 3xy and -12xy to get -9xy.

$$7x^{2}-9xy+6y^{2}-x^{3}-13x^{2}-3y^{2}-x_{2}$$

Combine 7x^{2} and -13x^{2} to get -6x^{2}.

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

Combine 6y^{2} and -3y^{2} to get 3y^{2}.

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