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

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

Evaluate

$$6y^{3}x^{5}$$

Solution Steps

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

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

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

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

Combine \frac{3}{2}xy and 2xy to get \frac{7}{2}xy.

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

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

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

Combine x^{4}y^{2} and -x^{4}y^{2} to get 0.

$$\left(y+\frac{7}{2}xy\right)\times 0+\left(-x\right)y^{3}\times 3x^{4}\left(-2\right)$$

Anything times zero gives zero.

$$0+\left(-x\right)y^{3}\times 3x^{4}\left(-2\right)$$

Multiply 3 and -2 to get -6.

$$0+\left(-x\right)y^{3}\left(-6\right)x^{4}$$

Anything plus zero gives itself.

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

Multiply -1 and -6 to get 6.

$$6xy^{3}x^{4}$$

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

$$6x^{5}y^{3}$$

Expand

$$6y^{3}x^{5}$$

Solution Steps

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

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

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

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

Combine \frac{3}{2}xy and 2xy to get \frac{7}{2}xy.

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

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

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

Combine x^{4}y^{2} and -x^{4}y^{2} to get 0.

$$\left(y+\frac{7}{2}xy\right)\times 0+\left(-x\right)y^{3}\times 3x^{4}\left(-2\right)$$

Anything times zero gives zero.

$$0+\left(-x\right)y^{3}\times 3x^{4}\left(-2\right)$$

Multiply 3 and -2 to get -6.

$$0+\left(-x\right)y^{3}\left(-6\right)x^{4}$$

Anything plus zero gives itself.

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

Multiply -1 and -6 to get 6.

$$6xy^{3}x^{4}$$

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

$$6x^{5}y^{3}$$