Solve 1/2xsqrt{y}left(-3xsqrt{y}-4ysqrt{x}right)+2x^2y-2/3yxsqrt{xy}

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

Factor

$$\frac{3yx^{2}-16\left(xy\right)^{\frac{3}{2}}}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{3x\sqrt{y}\left(-3x\sqrt{y}-4y\sqrt{x}\right)+12x^{2}y-4yx\sqrt{xy}}{6}$$

Consider 3x\sqrt{y}\left(-3x\sqrt{y}-4y\sqrt{x}\right)+12x^{2}y-4yx\sqrt{xy}. Factor out x\sqrt{y}.

$$x\sqrt{y}\left(3\left(-3x\sqrt{y}-4y\sqrt{x}\right)+12x\sqrt{y}-4\sqrt{y}\sqrt{xy}\right)$$

Rewrite the complete factored expression.

$$\frac{x\sqrt{y}\left(3\left(-3x\sqrt{y}-4y\sqrt{x}\right)+12x\sqrt{y}-4\sqrt{y}\sqrt{xy}\right)}{6}$$

Evaluate

$$-\frac{8\left(xy\right)^{\frac{3}{2}}}{3}+\frac{yx^{2}}{2}$$