Solve -7/5xy(-3/14xy)(+15/2x^2)+(-6/5x^2y+frac{7}{10}x^2y)(-frac{3}{2}x^2y)

$$- \frac{ 7 }{ 5 } xy(- \frac{ 3 }{ 14 } xy)(+ \frac{ 15 }{ 2 } { x }^{ 2 } )+(- \frac{ 6 }{ 5 } { x }^{ 2 } y+ \frac{ 7 }{ 10 } { x }^{ 2 } y)(- \frac{ 3 }{ 2 } { x }^{ 2 } y)$$

Evaluate

$$3y^{2}x^{4}$$

Solution Steps

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

$$-\frac{7}{5}x^{2}y\left(-\frac{3}{14}\right)y\times \frac{15}{2}x^{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{7}{5}x^{4}y\left(-\frac{3}{14}\right)y\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

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

$$-\frac{7}{5}x^{4}y^{2}\left(-\frac{3}{14}\right)\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Multiply -\frac{7}{5} and -\frac{3}{14} to get \frac{3}{10}.

$$\frac{3}{10}x^{4}y^{2}\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Multiply \frac{3}{10} and \frac{15}{2} to get \frac{9}{4}.

$$\frac{9}{4}x^{4}y^{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Combine -\frac{6}{5}x^{2}y and \frac{7}{10}x^{2}y to get -\frac{1}{2}x^{2}y.

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

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

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{2}yx^{2}y$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{4}yy$$

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

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{4}y^{2}$$

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

$$3x^{4}y^{2}$$

Expand

$$3y^{2}x^{4}$$

Solution Steps

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

$$-\frac{7}{5}x^{2}y\left(-\frac{3}{14}\right)y\times \frac{15}{2}x^{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-\frac{7}{5}x^{4}y\left(-\frac{3}{14}\right)y\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

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

$$-\frac{7}{5}x^{4}y^{2}\left(-\frac{3}{14}\right)\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Multiply -\frac{7}{5} and -\frac{3}{14} to get \frac{3}{10}.

$$\frac{3}{10}x^{4}y^{2}\times \frac{15}{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Multiply \frac{3}{10} and \frac{15}{2} to get \frac{9}{4}.

$$\frac{9}{4}x^{4}y^{2}+\left(-\frac{6}{5}x^{2}y+\frac{7}{10}x^{2}y\right)\left(-\frac{3}{2}\right)x^{2}y$$

Combine -\frac{6}{5}x^{2}y and \frac{7}{10}x^{2}y to get -\frac{1}{2}x^{2}y.

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

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

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{2}yx^{2}y$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{4}yy$$

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

$$\frac{9}{4}x^{4}y^{2}+\frac{3}{4}x^{4}y^{2}$$

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

$$3x^{4}y^{2}$$