Solve left(2x-yright)^2-4(x-y)(x+2y)

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

Evaluate

$$y\left(9y-8x\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.

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

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

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

Use the distributive property to multiply -4x+4y by x+2y and combine like terms.

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

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

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

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

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

Combine y^{2} and 8y^{2} to get 9y^{2}.

$$-8xy+9y^{2}$$

Expand

$$9y^{2}-8xy$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-y\right)^{2}.

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

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

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

Use the distributive property to multiply -4x+4y by x+2y and combine like terms.

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

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

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

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

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

Combine y^{2} and 8y^{2} to get 9y^{2}.

$$-8xy+9y^{2}$$