Solve frac{-9xsqrt{y}-12xysqrt{x}-4xysqrt{xy}+12x^2y}{6}

$$\frac { - 9 x \sqrt { y } - 12 x y \sqrt { x } - 4 x y \sqrt { x y } + 12 x ^ { 2 } y } { 6 }$$

Factor

$$\frac{-4\left(xy\right)^{\frac{3}{2}}+12yx^{2}-12yx^{\frac{3}{2}}-9\sqrt{y}x}{6}$$

Solution Steps

Consider -9x\sqrt{y}-12xy\sqrt{x}-4xy\sqrt{xy}+12x^{2}y. Factor out x\sqrt{y}.

$$x\sqrt{y}\left(-9-12\sqrt{y}\sqrt{x}-4\sqrt{y}\sqrt{xy}+12x\sqrt{y}\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(-9-12\sqrt{y}\sqrt{x}-4\sqrt{y}\sqrt{xy}+12x\sqrt{y}\right)\sqrt{y}}{6}$$

Evaluate

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