Solve (3x^3(-1/2y)+xy(5x^2-(-x^2)))(-2/3x)-y(-8x^4+2{x}^4)

$$(3 { x }^{ 3 } (- \frac{ 1 }{ 2 } y)+xy(5 { x }^{ 2 } -(- { x }^{ 2 } )))(- \frac{ 2 }{ 3 } x)-y(-8 { x }^{ 4 } +2 { x }^{ 4 } )$$

Evaluate

$$3yx^{4}$$

Solution Steps

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

$$\left(-\frac{3}{2}x^{3}y+xy\left(5x^{2}-\left(-x^{2}\right)\right)\right)\left(-\frac{2}{3}\right)x-y\left(-8x^{4}+2x^{4}\right)$$

Use the distributive property to multiply -\frac{3}{2}x^{3}y+xy\left(5x^{2}-\left(-x^{2}\right)\right) by -\frac{2}{3}.

$$\left(x^{3}y-\frac{2}{3}xy\left(5x^{2}-\left(-x^{2}\right)\right)\right)x-y\left(-8x^{4}+2x^{4}\right)$$

Use the distributive property to multiply x^{3}y-\frac{2}{3}xy\left(5x^{2}-\left(-x^{2}\right)\right) by x.

$$yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}-y\left(-8x^{4}+2x^{4}\right)$$

Combine -8x^{4} and 2x^{4} to get -6x^{4}.

$$yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}-y\left(-6\right)x^{4}$$

Combine yx^{4} and -y\left(-6\right)x^{4} to get 7yx^{4}.

$$7yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}$$

Multiply -1 and -1 to get 1.

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

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$7yx^{4}-\frac{2}{3}y\times 6x^{2}x^{2}$$

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

$$7yx^{4}-4yx^{2}x^{2}$$

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

$$7yx^{4}-4yx^{4}$$

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

$$3yx^{4}$$

Expand

$$3yx^{4}$$

Solution Steps

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

$$\left(-\frac{3}{2}x^{3}y+xy\left(5x^{2}-\left(-x^{2}\right)\right)\right)\left(-\frac{2}{3}\right)x-y\left(-8x^{4}+2x^{4}\right)$$

Use the distributive property to multiply -\frac{3}{2}x^{3}y+xy\left(5x^{2}-\left(-x^{2}\right)\right) by -\frac{2}{3}.

$$\left(x^{3}y-\frac{2}{3}xy\left(5x^{2}-\left(-x^{2}\right)\right)\right)x-y\left(-8x^{4}+2x^{4}\right)$$

Use the distributive property to multiply x^{3}y-\frac{2}{3}xy\left(5x^{2}-\left(-x^{2}\right)\right) by x.

$$yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}-y\left(-8x^{4}+2x^{4}\right)$$

Combine -8x^{4} and 2x^{4} to get -6x^{4}.

$$yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}-y\left(-6\right)x^{4}$$

Combine yx^{4} and -y\left(-6\right)x^{4} to get 7yx^{4}.

$$7yx^{4}-\frac{2}{3}y\left(5x^{2}-\left(-x^{2}\right)\right)x^{2}$$

Multiply -1 and -1 to get 1.

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

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$7yx^{4}-\frac{2}{3}y\times 6x^{2}x^{2}$$

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

$$7yx^{4}-4yx^{2}x^{2}$$

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

$$7yx^{4}-4yx^{4}$$

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

$$3yx^{4}$$