Solve ((2x-2y)^2-4(x+y)^2)div(2xy)^3

$$( ( 2 x - 2 y ) ^ { 2 } - 4 ( x + y ) ^ { 2 } ) \div ( 2 x y ) ^ { 3 }$$

Evaluate

$$-\frac{2}{\left(xy\right)^{2}}$$

Short Solution Steps

Expand \left(2xy\right)^{3}.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(2x-2y\right)^{2}-4\left(x+y\right)^{2}}{8x^{3}y^{3}}$$

Factor the expressions that are not already factored.

$$\frac{-2\times 2\times 4xy}{8x^{3}y^{3}}$$

Cancel out 2\times 2\times 2xy in both numerator and denominator.

$$\frac{-2}{x^{2}y^{2}}$$

Expand

$$-\frac{2}{\left(xy\right)^{2}}$$

Short Solution Steps

Expand \left(2xy\right)^{3}.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(2x-2y\right)^{2}-4\left(x+y\right)^{2}}{8x^{3}y^{3}}$$

Factor the expressions that are not already factored.

$$\frac{-2\times 2\times 4xy}{8x^{3}y^{3}}$$

Cancel out 2\times 2\times 2xy in both numerator and denominator.

$$\frac{-2}{x^{2}y^{2}}$$