Solve 5y^2+3y+5y-1/4y^2+1/3y^2+{y}_{}

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

Evaluate

$$\frac{61y^{2}}{12}+9y$$

Solution Steps

Combine 3y and 5y to get 8y.

$$5y^{2}+8y-\frac{1}{4}y^{2}+\frac{1}{3}y^{2}+y$$

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

$$\frac{19}{4}y^{2}+8y+\frac{1}{3}y^{2}+y$$

Combine \frac{19}{4}y^{2} and \frac{1}{3}y^{2} to get \frac{61}{12}y^{2}.

$$\frac{61}{12}y^{2}+8y+y$$

Combine 8y and y to get 9y.

$$\frac{61}{12}y^{2}+9y$$

Factor

$$\frac{y\left(61y+108\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{60y^{2}+36y+60y-3y^{2}+4y^{2}+12y}{12}$$

Consider 60y^{2}+36y+60y-3y^{2}+4y^{2}+12y. Factor out y.

$$y\left(61y+108\right)$$

Consider 60y+36+60-3y+4y+12. Multiply and combine like terms.

$$61y+108$$

Rewrite the complete factored expression.

$$\frac{y\left(61y+108\right)}{12}$$