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

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

Evaluate

$$2\left(x-y\right)\left(2x-2y-1\right)$$

Solution Steps

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

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

Use the distributive property to multiply 4 by x^{2}-2xy+y^{2}.

$$4x^{2}-8xy+4y^{2}-2\left(x-y\right)$$

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

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply 4 by x^{2}-2xy+y^{2}.

$$4x^{2}-8xy+4y^{2}-2\left(x-y\right)$$

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

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