Solve (x^2-1/3x^2-4/3x^2)*((1/2xy^2)*(-8{x}^3)-({x}^2{y}^2)*(4{x}^2))

$$( { x }^{ 2 } - \frac{ 1 }{ 3 } { x }^{ 2 } - \frac{ 4 }{ 3 } { x }^{ 2 } ) \times (( \frac{ 1 }{ 2 } x { y }^{ 2 } ) \times (-8 { x }^{ 3 } )-( { x }^{ 2 } { y }^{ 2 } ) \times (4 { x }^{ 2 } ))$$

Evaluate

$$\frac{16y^{2}x^{6}}{3}$$

Solution Steps

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

$$\left(x^{2}-\frac{1}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{2}y^{2}\times 4x^{2}\right)$$

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

$$\left(x^{2}-\frac{1}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

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

$$\left(\frac{2}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

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

$$-\frac{2}{3}x^{2}\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

Multiply \frac{1}{2} and -8 to get -4.

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

Combine -4x^{4}y^{2} and -x^{4}y^{2}\times 4 to get -8x^{4}y^{2}.

$$-\frac{2}{3}x^{2}\left(-8\right)x^{4}y^{2}$$

Multiply -\frac{2}{3} and -8 to get \frac{16}{3}.

$$\frac{16}{3}x^{2}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{16}{3}x^{6}y^{2}$$

Expand

$$\frac{16y^{2}x^{6}}{3}$$

Solution Steps

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

$$\left(x^{2}-\frac{1}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{2}y^{2}\times 4x^{2}\right)$$

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

$$\left(x^{2}-\frac{1}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

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

$$\left(\frac{2}{3}x^{2}-\frac{4}{3}x^{2}\right)\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

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

$$-\frac{2}{3}x^{2}\left(\frac{1}{2}x^{4}y^{2}\left(-8\right)-x^{4}y^{2}\times 4\right)$$

Multiply \frac{1}{2} and -8 to get -4.

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

Combine -4x^{4}y^{2} and -x^{4}y^{2}\times 4 to get -8x^{4}y^{2}.

$$-\frac{2}{3}x^{2}\left(-8\right)x^{4}y^{2}$$

Multiply -\frac{2}{3} and -8 to get \frac{16}{3}.

$$\frac{16}{3}x^{2}x^{4}y^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{16}{3}x^{6}y^{2}$$