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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply 2 by x+y.

$$\left(2x+2y\right)\left(-x-y\right)-\left(2x+y\right)\left(-2x+y\right)$$

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

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

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

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

Combine 2xy and -2yx to get 0.

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

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

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

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

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

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

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

Multiply 2 and -1 to get -2.

$$-2xx-2xy+2y\left(-1\right)x-3y^{2}+4x^{2}$$

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

$$-2x^{2}-2xy+2y\left(-1\right)x-3y^{2}+4x^{2}$$

Multiply 2 and -1 to get -2.

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

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

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply 2 by x+y.

$$\left(2x+2y\right)\left(-x-y\right)-\left(2x+y\right)\left(-2x+y\right)$$

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

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

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

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

Combine 2xy and -2yx to get 0.

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

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

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

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

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

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

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

Multiply 2 and -1 to get -2.

$$-2xx-2xy+2y\left(-1\right)x-3y^{2}+4x^{2}$$

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

$$-2x^{2}-2xy+2y\left(-1\right)x-3y^{2}+4x^{2}$$

Multiply 2 and -1 to get -2.

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

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

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

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

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