Solve (2/3x^{6}y^5):(-4/15x^4y^4)-2(-xy)(-x)+2xy(-3x)-3/2x^2y=

$$( \frac { 2 } { 3 } x ^ { 6 } y ^ { 5 } ) : ( - \frac { 4 } { 15 } x ^ { 4 } y ^ { 4 } ) - 2 ( - x y ) ( - x ) + 2 x y ( - 3 x ) - \frac { 3 } { 2 } x ^ { 2 } y =$$

Evaluate

$$-12yx^{2}$$

Solution Steps

Multiply -x and -x to get \left(-x\right)^{2}.

$$\frac{\frac{2}{3}x^{6}y^{5}}{-\frac{4}{15}x^{4}y^{4}}-2\left(-x\right)^{2}y+2xy\left(-3\right)x-\frac{3}{2}x^{2}y$$

Multiply x and x to get x^{2}.

$$\frac{\frac{2}{3}x^{6}y^{5}}{-\frac{4}{15}x^{4}y^{4}}-2\left(-x\right)^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Cancel out x^{4}y^{4} in both numerator and denominator.

$$\frac{\frac{2}{3}yx^{2}}{-\frac{4}{15}}-2\left(-x\right)^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Divide \frac{2}{3}yx^{2} by -\frac{4}{15} by multiplying \frac{2}{3}yx^{2} by the reciprocal of -\frac{4}{15}.

$$\frac{\frac{2}{3}yx^{2}\times 15}{-4}-2\left(-x\right)^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Multiply \frac{2}{3} and 15 to get 10.

$$\frac{10yx^{2}}{-4}-2\left(-x\right)^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Divide 10yx^{2} by -4 to get -\frac{5}{2}yx^{2}.

$$-\frac{5}{2}yx^{2}-2\left(-x\right)^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Calculate -x to the power of 2 and get x^{2}.

$$-\frac{5}{2}yx^{2}-2x^{2}y+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Combine -\frac{5}{2}yx^{2} and -2x^{2}y to get -\frac{9}{2}yx^{2}.

$$-\frac{9}{2}yx^{2}+2x^{2}y\left(-3\right)-\frac{3}{2}x^{2}y$$

Multiply 2 and -3 to get -6.

$$-\frac{9}{2}yx^{2}-6x^{2}y-\frac{3}{2}x^{2}y$$

Combine -\frac{9}{2}yx^{2} and -6x^{2}y to get -\frac{21}{2}yx^{2}.

$$-\frac{21}{2}yx^{2}-\frac{3}{2}x^{2}y$$

Combine -\frac{21}{2}yx^{2} and -\frac{3}{2}x^{2}y to get -12yx^{2}.

$$-12yx^{2}$$

Differentiate w.r.t. x

$$-24xy$$