Solve -x^{3}y+2xy(-2/3x^2)+6x^2(-3/8xy)-y(-2x^3-1/4x^3)

$$- x ^ { 3 } y + 2 x y ( - \frac { 2 } { 3 } x ^ { 2 } ) + 6 x ^ { 2 } ( - \frac { 3 } { 8 } x y ) - y ( - 2 x ^ { 3 } - \frac { 1 } { 4 } x ^ { 3 } )$$

Evaluate

$$-\frac{7yx^{3}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-x^{3}\right)y+2x^{3}y\left(-\frac{2}{3}\right)+6x^{2}\left(-\frac{3}{8}\right)xy-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(-x^{3}\right)y+2x^{3}y\left(-\frac{2}{3}\right)+6x^{3}\left(-\frac{3}{8}\right)y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Multiply 2 and -\frac{2}{3} to get -\frac{4}{3}.

$$\left(-x^{3}\right)y-\frac{4}{3}x^{3}y+6x^{3}\left(-\frac{3}{8}\right)y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Multiply 6 and -\frac{3}{8} to get -\frac{9}{4}.

$$\left(-x^{3}\right)y-\frac{4}{3}x^{3}y-\frac{9}{4}x^{3}y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Combine -\frac{4}{3}x^{3}y and -\frac{9}{4}x^{3}y to get -\frac{43}{12}x^{3}y.

$$\left(-x^{3}\right)y-\frac{43}{12}x^{3}y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Combine -2x^{3} and -\frac{1}{4}x^{3} to get -\frac{9}{4}x^{3}.

$$\left(-x^{3}\right)y-\frac{43}{12}x^{3}y-y\left(-\frac{9}{4}\right)x^{3}$$

Combine -\frac{43}{12}x^{3}y and -y\left(-\frac{9}{4}\right)x^{3} to get -\frac{4}{3}x^{3}y.

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

Combine -x^{3}y and -\frac{4}{3}x^{3}y to get -\frac{7}{3}x^{3}y.

$$-\frac{7}{3}x^{3}y$$

Expand

$$-\frac{7yx^{3}}{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\left(-x^{3}\right)y+2x^{3}y\left(-\frac{2}{3}\right)+6x^{2}\left(-\frac{3}{8}\right)xy-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(-x^{3}\right)y+2x^{3}y\left(-\frac{2}{3}\right)+6x^{3}\left(-\frac{3}{8}\right)y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Multiply 2 and -\frac{2}{3} to get -\frac{4}{3}.

$$\left(-x^{3}\right)y-\frac{4}{3}x^{3}y+6x^{3}\left(-\frac{3}{8}\right)y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Multiply 6 and -\frac{3}{8} to get -\frac{9}{4}.

$$\left(-x^{3}\right)y-\frac{4}{3}x^{3}y-\frac{9}{4}x^{3}y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Combine -\frac{4}{3}x^{3}y and -\frac{9}{4}x^{3}y to get -\frac{43}{12}x^{3}y.

$$\left(-x^{3}\right)y-\frac{43}{12}x^{3}y-y\left(-2x^{3}-\frac{1}{4}x^{3}\right)$$

Combine -2x^{3} and -\frac{1}{4}x^{3} to get -\frac{9}{4}x^{3}.

$$\left(-x^{3}\right)y-\frac{43}{12}x^{3}y-y\left(-\frac{9}{4}\right)x^{3}$$

Combine -\frac{43}{12}x^{3}y and -y\left(-\frac{9}{4}\right)x^{3} to get -\frac{4}{3}x^{3}y.

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

Combine -x^{3}y and -\frac{4}{3}x^{3}y to get -\frac{7}{3}x^{3}y.

$$-\frac{7}{3}x^{3}y$$