Solve (2/8y^2-2/4y)(2/3y+4)-2/4y(y^2-4y)]-(2y^2-2y)

$$( \frac { 2 } { 8 } y ^ { 2 } - \frac { 2 } { 4 } y ) ( \frac { 2 } { 3 } y + 4 ) - \frac { 2 } { 4 } y ( y ^ { 2 } - 4 y ) ] - ( 2 y ^ { 2 } - 2 y )$$

Evaluate

$$\frac{y\left(-y^{2}+8y-6\right)}{3}$$

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Use the distributive property to multiply \frac{1}{4}y^{2}-\frac{1}{2}y by \frac{2}{3}y+4 and combine like terms.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{2}{4}y\left(y^{2}-4y\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{1}{2}y\left(y^{2}-4y\right)$$

Use the distributive property to multiply -\frac{1}{2}y by y^{2}-4y.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{1}{2}y^{3}+2y^{2}$$

Combine \frac{1}{6}y^{3} and -\frac{1}{2}y^{3} to get -\frac{1}{3}y^{3}.

$$-\frac{1}{3}y^{3}+\frac{2}{3}y^{2}-2y+2y^{2}$$

Combine \frac{2}{3}y^{2} and 2y^{2} to get \frac{8}{3}y^{2}.

$$-\frac{1}{3}y^{3}+\frac{8}{3}y^{2}-2y$$

Expand

$$-\frac{y^{3}}{3}+\frac{8y^{2}}{3}-2y$$

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Use the distributive property to multiply \frac{1}{4}y^{2}-\frac{1}{2}y by \frac{2}{3}y+4 and combine like terms.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{2}{4}y\left(y^{2}-4y\right)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{1}{2}y\left(y^{2}-4y\right)$$

Use the distributive property to multiply -\frac{1}{2}y by y^{2}-4y.

$$\frac{1}{6}y^{3}+\frac{2}{3}y^{2}-2y-\frac{1}{2}y^{3}+2y^{2}$$

Combine \frac{1}{6}y^{3} and -\frac{1}{2}y^{3} to get -\frac{1}{3}y^{3}.

$$-\frac{1}{3}y^{3}+\frac{2}{3}y^{2}-2y+2y^{2}$$

Combine \frac{2}{3}y^{2} and 2y^{2} to get \frac{8}{3}y^{2}.

$$-\frac{1}{3}y^{3}+\frac{8}{3}y^{2}-2y$$