Solve 2/5x^2(-1/2xy^3)+(1-2/5)x^3y^3-(-2/3xy)(-frac{3}{10}{x}^2{y}^2)-2{x}^3{y}^3

$$\frac{ 2 }{ 5 } { x }^{ 2 } (- \frac{ 1 }{ 2 } x { y }^{ 3 } )+(1- \frac{ 2 }{ 5 } ) { x }^{ 3 } { y }^{ 3 } -(- \frac{ 2 }{ 3 } xy)(- \frac{ 3 }{ 10 } { x }^{ 2 } { y }^{ 2 } )-2 { x }^{ 3 } { y }^{ 3 }$$

Evaluate

$$-\frac{9\left(xy\right)^{3}}{5}$$

Solution Steps

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}xy\left(-\frac{3}{10}\right)x^{2}y^{2}\right)-2x^{3}y^{3}$$

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y\left(-\frac{3}{10}\right)y^{2}\right)-2x^{3}y^{3}$$

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Multiply \frac{2}{5} and -\frac{1}{2} to get -\frac{1}{5}.

$$-\frac{1}{5}x^{3}y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Subtract \frac{2}{5} from 1 to get \frac{3}{5}.

$$-\frac{1}{5}x^{3}y^{3}+\frac{3}{5}x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Combine -\frac{1}{5}x^{3}y^{3} and \frac{3}{5}x^{3}y^{3} to get \frac{2}{5}x^{3}y^{3}.

$$\frac{2}{5}x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Multiply -\frac{2}{3} and -\frac{3}{10} to get \frac{1}{5}.

$$\frac{2}{5}x^{3}y^{3}-\frac{1}{5}x^{3}y^{3}-2x^{3}y^{3}$$

Combine \frac{2}{5}x^{3}y^{3} and -\frac{1}{5}x^{3}y^{3} to get \frac{1}{5}x^{3}y^{3}.

$$\frac{1}{5}x^{3}y^{3}-2x^{3}y^{3}$$

Combine \frac{1}{5}x^{3}y^{3} and -2x^{3}y^{3} to get -\frac{9}{5}x^{3}y^{3}.

$$-\frac{9}{5}x^{3}y^{3}$$

Expand

$$-\frac{9\left(xy\right)^{3}}{5}$$

Solution Steps

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}xy\left(-\frac{3}{10}\right)x^{2}y^{2}\right)-2x^{3}y^{3}$$

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y\left(-\frac{3}{10}\right)y^{2}\right)-2x^{3}y^{3}$$

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

$$\frac{2}{5}x^{3}\left(-\frac{1}{2}\right)y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Multiply \frac{2}{5} and -\frac{1}{2} to get -\frac{1}{5}.

$$-\frac{1}{5}x^{3}y^{3}+\left(1-\frac{2}{5}\right)x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Subtract \frac{2}{5} from 1 to get \frac{3}{5}.

$$-\frac{1}{5}x^{3}y^{3}+\frac{3}{5}x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Combine -\frac{1}{5}x^{3}y^{3} and \frac{3}{5}x^{3}y^{3} to get \frac{2}{5}x^{3}y^{3}.

$$\frac{2}{5}x^{3}y^{3}-\left(-\frac{2}{3}x^{3}y^{3}\left(-\frac{3}{10}\right)\right)-2x^{3}y^{3}$$

Multiply -\frac{2}{3} and -\frac{3}{10} to get \frac{1}{5}.

$$\frac{2}{5}x^{3}y^{3}-\frac{1}{5}x^{3}y^{3}-2x^{3}y^{3}$$

Combine \frac{2}{5}x^{3}y^{3} and -\frac{1}{5}x^{3}y^{3} to get \frac{1}{5}x^{3}y^{3}.

$$\frac{1}{5}x^{3}y^{3}-2x^{3}y^{3}$$

Combine \frac{1}{5}x^{3}y^{3} and -2x^{3}y^{3} to get -\frac{9}{5}x^{3}y^{3}.

$$-\frac{9}{5}x^{3}y^{3}$$