Solve -(x^2-4^2)+xy+(-2x^2+3xy)-[-4^2+xy]

$$- ( x ^ { 2 } - 4 ^ { 2 } ) + x y + ( - 2 x ^ { 2 } + 3 x y ) - [ - 4 ^ { 2 } + x y ]$$

Evaluate

$$32+3xy-3x^{2}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$-\left(x^{2}-16\right)+xy-2x^{2}+3xy-\left(-4^{2}+xy\right)$$

To find the opposite of x^{2}-16, find the opposite of each term.

$$-x^{2}+16+xy-2x^{2}+3xy-\left(-4^{2}+xy\right)$$

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

$$-3x^{2}+16+xy+3xy-\left(-4^{2}+xy\right)$$

Combine xy and 3xy to get 4xy.

$$-3x^{2}+16+4xy-\left(-4^{2}+xy\right)$$

Calculate 4 to the power of 2 and get 16.

$$-3x^{2}+16+4xy-\left(-16+xy\right)$$

To find the opposite of -16+xy, find the opposite of each term.

$$-3x^{2}+16+4xy+16-xy$$

Add 16 and 16 to get 32.

$$-3x^{2}+32+4xy-xy$$

Combine 4xy and -xy to get 3xy.

$$-3x^{2}+32+3xy$$

Expand

$$32+3xy-3x^{2}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$-\left(x^{2}-16\right)+xy-2x^{2}+3xy-\left(-4^{2}+xy\right)$$

To find the opposite of x^{2}-16, find the opposite of each term.

$$-x^{2}+16+xy-2x^{2}+3xy-\left(-4^{2}+xy\right)$$

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

$$-3x^{2}+16+xy+3xy-\left(-4^{2}+xy\right)$$

Combine xy and 3xy to get 4xy.

$$-3x^{2}+16+4xy-\left(-4^{2}+xy\right)$$

Calculate 4 to the power of 2 and get 16.

$$-3x^{2}+16+4xy-\left(-16+xy\right)$$

To find the opposite of -16+xy, find the opposite of each term.

$$-3x^{2}+16+4xy+16-xy$$

Add 16 and 16 to get 32.

$$-3x^{2}+32+4xy-xy$$

Combine 4xy and -xy to get 3xy.

$$-3x^{2}+32+3xy$$