Solve (x+y)(-x-y)-(2x+y)(-2x+y)

$$( x + y ) ( - x - y ) - ( 2 x + y ) ( - 2 x + y )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+y by each term of -x-y.

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

Apply the distributive property by multiplying each term of 2x+y by each term of -2x+y.

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

Combine 2xy and -2yx to get 0.

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

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

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

The opposite of -4x^{2} is 4x^{2}.

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

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

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

Multiply x and x to get x^{2}.

$$x^{2}\left(-1\right)-xy+y\left(-1\right)x-2y^{2}+4x^{2}$$

Combine -xy and y\left(-1\right)x to get -2xy.

$$x^{2}\left(-1\right)-2xy-2y^{2}+4x^{2}$$

Combine x^{2}\left(-1\right) and 4x^{2} to get 3x^{2}.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of x+y by each term of -x-y.

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

Apply the distributive property by multiplying each term of 2x+y by each term of -2x+y.

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

Combine 2xy and -2yx to get 0.

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

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

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

The opposite of -4x^{2} is 4x^{2}.

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

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

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

Multiply x and x to get x^{2}.

$$x^{2}\left(-1\right)-xy+y\left(-1\right)x-2y^{2}+4x^{2}$$

Combine -xy and y\left(-1\right)x to get -2xy.

$$x^{2}\left(-1\right)-2xy-2y^{2}+4x^{2}$$

Combine x^{2}\left(-1\right) and 4x^{2} to get 3x^{2}.

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