Solve (2/3y^3+3/4y^2+1/2)+(1/3y^3+frac{1}{5}y^2-frac{1}{6})

$$( \frac { 2 } { 3 } y ^ { 3 } + \frac { 3 } { 4 } y ^ { 2 } + \frac { 1 } { 2 } ) + ( \frac { 1 } { 3 } y ^ { 3 } + \frac { 1 } { 5 } y ^ { 2 } - \frac { 1 } { 6 } )$$

Evaluate

$$y^{3}+\frac{19y^{2}}{20}+\frac{1}{3}$$

Solution Steps

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

$$y^{3}+\frac{3}{4}y^{2}+\frac{1}{2}+\frac{1}{5}y^{2}-\frac{1}{6}$$

Combine \frac{3}{4}y^{2} and \frac{1}{5}y^{2} to get \frac{19}{20}y^{2}.

$$y^{3}+\frac{19}{20}y^{2}+\frac{1}{2}-\frac{1}{6}$$

Subtract \frac{1}{6} from \frac{1}{2} to get \frac{1}{3}.

$$y^{3}+\frac{19}{20}y^{2}+\frac{1}{3}$$

Factor

$$\frac{60y^{3}+57y^{2}+20}{60}$$

Solution Steps

Factor out \frac{1}{60}. Polynomial 60y^{3}+57y^{2}+20 is not factored since it does not have any rational roots.

$$\frac{60y^{3}+57y^{2}+20}{60}$$