Solve (-2/5xy^{2}+3/10xy^{2}-2/15xy^{2})(-1/7x^{3}y+frac{1}{14}x^3y)(-15x)+(-3xy^2)(+2x^2)(-frac{1}{4}x^2y)

$$( - \frac { 2 } { 5 } x y ^ { 2 } + \frac { 3 } { 10 } x y ^ { 2 } - \frac { 2 } { 15 } x y ^ { 2 } ) ( - \frac { 1 } { 7 } x ^ { 3 } y + \frac { 1 } { 14 } x ^ { 3 } y ) ( - 15 x ) + ( - 3 x y ^ { 2 } ) ( + 2 x ^ { 2 } ) ( - \frac { 1 } { 4 } x ^ { 2 } y )$$

Evaluate

$$\frac{5y^{3}x^{5}}{4}$$

Solution Steps

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

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{3}y^{2}\times 2\left(-\frac{1}{4}\right)x^{2}y$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{2}\times 2\left(-\frac{1}{4}\right)y$$

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

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{2}{5}xy^{2} and \frac{3}{10}xy^{2} to get -\frac{1}{10}xy^{2}.

$$\left(-\frac{1}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{1}{10}xy^{2} and -\frac{2}{15}xy^{2} to get -\frac{7}{30}xy^{2}.

$$-\frac{7}{30}xy^{2}\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{1}{7}x^{3}y and \frac{1}{14}x^{3}y to get -\frac{1}{14}x^{3}y.

$$-\frac{7}{30}xy^{2}\left(-\frac{1}{14}\right)x^{3}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply -\frac{7}{30} and -\frac{1}{14} to get \frac{1}{60}.

$$\frac{1}{60}xy^{2}x^{3}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{60}x^{4}y^{2}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

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

$$\frac{1}{60}x^{4}y^{3}\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply \frac{1}{60} and -15 to get -\frac{1}{4}.

$$-\frac{1}{4}x^{4}y^{3}x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{1}{4}x^{5}y^{3}-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply -3 and 2 to get -6.

$$-\frac{1}{4}x^{5}y^{3}-6x^{5}y^{3}\left(-\frac{1}{4}\right)$$

Multiply -6 and -\frac{1}{4} to get \frac{3}{2}.

$$-\frac{1}{4}x^{5}y^{3}+\frac{3}{2}x^{5}y^{3}$$

Combine -\frac{1}{4}x^{5}y^{3} and \frac{3}{2}x^{5}y^{3} to get \frac{5}{4}x^{5}y^{3}.

$$\frac{5}{4}x^{5}y^{3}$$

Expand

$$\frac{5y^{3}x^{5}}{4}$$

Solution Steps

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

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{3}y^{2}\times 2\left(-\frac{1}{4}\right)x^{2}y$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{2}\times 2\left(-\frac{1}{4}\right)y$$

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

$$\left(-\frac{2}{5}xy^{2}+\frac{3}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{2}{5}xy^{2} and \frac{3}{10}xy^{2} to get -\frac{1}{10}xy^{2}.

$$\left(-\frac{1}{10}xy^{2}-\frac{2}{15}xy^{2}\right)\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{1}{10}xy^{2} and -\frac{2}{15}xy^{2} to get -\frac{7}{30}xy^{2}.

$$-\frac{7}{30}xy^{2}\left(-\frac{1}{7}x^{3}y+\frac{1}{14}x^{3}y\right)\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Combine -\frac{1}{7}x^{3}y and \frac{1}{14}x^{3}y to get -\frac{1}{14}x^{3}y.

$$-\frac{7}{30}xy^{2}\left(-\frac{1}{14}\right)x^{3}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply -\frac{7}{30} and -\frac{1}{14} to get \frac{1}{60}.

$$\frac{1}{60}xy^{2}x^{3}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{1}{60}x^{4}y^{2}y\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

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

$$\frac{1}{60}x^{4}y^{3}\left(-15\right)x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply \frac{1}{60} and -15 to get -\frac{1}{4}.

$$-\frac{1}{4}x^{4}y^{3}x-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{1}{4}x^{5}y^{3}-3x^{5}y^{3}\times 2\left(-\frac{1}{4}\right)$$

Multiply -3 and 2 to get -6.

$$-\frac{1}{4}x^{5}y^{3}-6x^{5}y^{3}\left(-\frac{1}{4}\right)$$

Multiply -6 and -\frac{1}{4} to get \frac{3}{2}.

$$-\frac{1}{4}x^{5}y^{3}+\frac{3}{2}x^{5}y^{3}$$

Combine -\frac{1}{4}x^{5}y^{3} and \frac{3}{2}x^{5}y^{3} to get \frac{5}{4}x^{5}y^{3}.

$$\frac{5}{4}x^{5}y^{3}$$