Solve 2x(2x-y)-4(x-y)(x+2y)

$$2 x ( 2 x - y ) - 4 ( x - y ) ( x + 2 y )$$

Evaluate

$$2y\left(4y-3x\right)$$

Solution Steps

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

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

Use the distributive property to multiply -4 by x-y.

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

Apply the distributive property by multiplying each term of -4x+4y by each term of x+2y.

$$4x^{2}-2xy-4x^{2}-8xy+4yx+8y^{2}$$

Combine -8xy and 4yx to get -4xy.

$$4x^{2}-2xy-4x^{2}-4xy+8y^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2xy-4xy+8y^{2}$$

Combine -2xy and -4xy to get -6xy.

$$-6xy+8y^{2}$$

Expand

$$8y^{2}-6xy$$

Solution Steps

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

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

Use the distributive property to multiply -4 by x-y.

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

Apply the distributive property by multiplying each term of -4x+4y by each term of x+2y.

$$4x^{2}-2xy-4x^{2}-8xy+4yx+8y^{2}$$

Combine -8xy and 4yx to get -4xy.

$$4x^{2}-2xy-4x^{2}-4xy+8y^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2xy-4xy+8y^{2}$$

Combine -2xy and -4xy to get -6xy.

$$-6xy+8y^{2}$$