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

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

Evaluate

$$2y^{2}+xy-9x^{2}$$

Solution Steps

To find the opposite of 5x^{2}+3xy-4y^{2}, find the opposite of each term.

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

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

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

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

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

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

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

Combine -5x^{2} and -4x^{2} to get -9x^{2}.

$$-9x^{2}-3xy+4y^{2}-2y^{2}+4xy$$

Combine 4y^{2} and -2y^{2} to get 2y^{2}.

$$-9x^{2}-3xy+2y^{2}+4xy$$

Combine -3xy and 4xy to get xy.

$$-9x^{2}+xy+2y^{2}$$

Expand

$$2y^{2}+xy-9x^{2}$$

Solution Steps

To find the opposite of 5x^{2}+3xy-4y^{2}, find the opposite of each term.

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

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

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

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

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

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

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

Combine -5x^{2} and -4x^{2} to get -9x^{2}.

$$-9x^{2}-3xy+4y^{2}-2y^{2}+4xy$$

Combine 4y^{2} and -2y^{2} to get 2y^{2}.

$$-9x^{2}-3xy+2y^{2}+4xy$$

Combine -3xy and 4xy to get xy.

$$-9x^{2}+xy+2y^{2}$$