Solve =[(2x^{2}y^{2}+3/4x^{2}y^{2}+x^{2}y^{2})(1/3x+x)+(-3/2y+y)(-3x^3y+7x^3y)]+3x^3y^2

$$= [ ( 2 x ^ { 2 } y ^ { 2 } + \frac { 3 } { 4 } x ^ { 2 } y ^ { 2 } + x ^ { 2 } y ^ { 2 } ) ( \frac { 1 } { 3 } x + x ) + ( - \frac { 3 } { 2 } y + y ) ( - 3 x ^ { 3 } y + 7 x ^ { 3 } y ) ] + 3 x ^ { 3 } y ^ { 2 }$$

Evaluate

$$6y^{2}x^{3}$$

Solution Steps

Combine 2x^{2}y^{2} and \frac{3}{4}x^{2}y^{2} to get \frac{11}{4}x^{2}y^{2}.

$$\left(\frac{11}{4}x^{2}y^{2}+x^{2}y^{2}\right)\left(\frac{1}{3}x+x\right)+\left(-\frac{3}{2}y+y\right)\left(-3x^{3}y+7x^{3}y\right)+3x^{3}y^{2}$$

Combine \frac{11}{4}x^{2}y^{2} and x^{2}y^{2} to get \frac{15}{4}x^{2}y^{2}.

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

Combine \frac{1}{3}x and x to get \frac{4}{3}x.

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

Multiply \frac{15}{4} and \frac{4}{3} to get 5.

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

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

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

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

$$5x^{3}y^{2}-\frac{1}{2}y\left(-3x^{3}y+7x^{3}y\right)+3x^{3}y^{2}$$

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

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

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

$$5x^{3}y^{2}-2yx^{3}y+3x^{3}y^{2}$$

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

$$5x^{3}y^{2}-2y^{2}x^{3}+3x^{3}y^{2}$$

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

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

Combine 3x^{3}y^{2} and 3x^{3}y^{2} to get 6x^{3}y^{2}.

$$6x^{3}y^{2}$$

Expand

$$6y^{2}x^{3}$$

Solution Steps

Combine 2x^{2}y^{2} and \frac{3}{4}x^{2}y^{2} to get \frac{11}{4}x^{2}y^{2}.

$$\left(\frac{11}{4}x^{2}y^{2}+x^{2}y^{2}\right)\left(\frac{1}{3}x+x\right)+\left(-\frac{3}{2}y+y\right)\left(-3x^{3}y+7x^{3}y\right)+3x^{3}y^{2}$$

Combine \frac{11}{4}x^{2}y^{2} and x^{2}y^{2} to get \frac{15}{4}x^{2}y^{2}.

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

Combine \frac{1}{3}x and x to get \frac{4}{3}x.

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

Multiply \frac{15}{4} and \frac{4}{3} to get 5.

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

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

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

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

$$5x^{3}y^{2}-\frac{1}{2}y\left(-3x^{3}y+7x^{3}y\right)+3x^{3}y^{2}$$

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

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

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

$$5x^{3}y^{2}-2yx^{3}y+3x^{3}y^{2}$$

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

$$5x^{3}y^{2}-2y^{2}x^{3}+3x^{3}y^{2}$$

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

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

Combine 3x^{3}y^{2} and 3x^{3}y^{2} to get 6x^{3}y^{2}.

$$6x^{3}y^{2}$$